1An Introduction to Applicative Universal Grammar

Bernard Paul SypniewskiRowan University

Copyright Bernard Paul Sypniewski, Woodbine, NJ 08270 1999Freely distributable for educational purposes

2Introduction

Sebastian Shaumyan's Applicable Universal Grammar (AUG) has generated considerableinterest but the technical nature of his novel description of language has discouraged many linguistsfrom investigating AUG in any thorough way. This monograph was written to make it easier for thosecurious about AUG to understand this interesting linguistic theory.

The primary source for AUG is A Semiotic Theory of Language Shaumyan (1987); thismonograph also relies on papers written by or co-authored by Professor Shaumyan since thepublication of A Semiotic Theory of Language. Despite the complexities of the text, the book is onlyan outline of AUG and its basic notions. Shaumyan currently plans a series of books to expandon his 1987 work. This monograph does not include the same detail as Shaumyan (1987).Certain portions of the original text, which, in some cases, are substantial in size, will be touchedupon only lightly. For example, AUG depends on combinatory logic. Combinatory logic is moreadvanced than the logic taught in schools. While an understanding of combinatory logic will satisfythe reader that Shaumyan rests AUG on a sound logical basis, an understanding of combinatorylogic is not necessary for an appreciation of AUG. Shaumyan illustrates his book with many linguisticexamples. I will omit most of the examples in Shaumyan (1987) in this monograph; I urge theinterested reader to refer to the original text for examples beyond those provided here.

I will describe AUG roughly in the order in Shaumyan (1987). Briefly, that order is:

A description of the semiotic theory of language; Phonology; Genotype Grammar; Phenotype Grammar; and Methodology.

A number of technical expressions1, e.g., genotype and phenotype grammar, may be unfamiliar tothe reader, especially in the sense that they are used in AUG. I will define these expressionswhen necessary for the understanding of the underlying theory.

Part 1 - An Overview of the Semiotic Theory of Language

AUG is not a theory about the workings of any particular language. AUG explainswhat is common to the way that all languages work; hence, the word universal in the nameApplicative Universal Grammar. AUG is a new way of looking at language that is frequently atodds with established linguistic theories. AUG analyzes the semiotic properties of languagewhile other systems, e.g., Generative Transformational Grammar, ignore the semiotics oflanguage. We will see that the semiotic properties of language are not additions to linguistics butare fundamental to the understanding of the operations inherent in all languages. AUG has twomajor components: applicative grammar and a two level phonology. Applicative grammar,itself, has two major components:

a formal calculus which contains the notions of inherent syntactic functions and thesuperposition of functions, and

a series of semiotic laws which constrain the calculus.

1 I will use the word expression for technical words andphrases. AUG uses the word term in a technical sense. I wishto avoid the obvious possibility of confusion

3Taken together, these components explain language and linguistic phenomena that aredifficult to explain or are inexplicable using other linguistic theories. While a semiotic analysisof language is capable of describing artificial languages and languages which non-humans(bees, ants, apes, etc.) might be capable of using, AUG is a theory limited to human language.For AUG, natural language is a culturally determined, mental phenomenon. Shaumyan(1987) contains a six part semiotic definition of language. Shaumyan and Sypniewski (1995)contains a somewhat different definition of natural language. Despite the differences in detail,these two definitions are complementary. The semiotic definition of language in Shaumyan(1987:2) posits a sign system with the following properties:

two semiotic strata; sequencing; use of rules; structure; hierarchical stratification; and semiotic relevance.

Shaumyan and Sypniewski (1995:1) gives the following definition for natural language: Natural languages are instruments of communication that transpose - each in its own way - anunanalyzed continuum of human experience into a system of discrete bilateral linguistic units.Each linguistic unit is a concept linked to a phonic segment - the sign of the concept. Thesign, in turn, is represented by phonemes - discrete acoustic distinctive elements.

In this monograph, I will rely on the original six-part semiotic definition of language, but I will alsodescribe the notion of linguistic unit mentioned in the latter definition, since it is slightly betterdeveloped in the paper than in the original text.

Two Semiotic Strata

Since AUG is a semiotic theory, the most basic notion in AUG is the notion of the sign. Itis crucial to understand that signs and meanings are not things. Rather, a sign and itsmeaning populate a reciprocal relation, referred to as the sign of: meaning of relation, if weexamine the relation from the point of view of the sign, or the meaning of: sign of relation if weexamine it from the viewpoint of the meaning. AUG emphasizes that the relation is moreimportant to linguistics than the sign entity; AUG specifically denies that there is such a class ofentities that have certain inherent properties that can be called "signs". Shaumyan andSypniewski (1995:1) AUG differs from other linguistic theories by emphasizing relationsrather than entities. Confusing sign with sign of will make AUG more difficult to understand. Icannot overstress how important it is to understand that AUG describes linguistic relations ratherthan "things". In many linguistic theories, things like words or phrases have inherent properties.In AUG, linguistic objects or expressions only exist in relation to other linguistic objects orexpressions. If there is no relation, there is nothing for AUG to concern itself about.

For AUG, the description of sign is different than descriptions of the sign in other semiotictheories or philosophies. For example, Peirce talks about a sign as an entity and insists that itbe connected with an object which he often defines in tangible terms, see, e.g. Peirce(1991:240-241) Peirce's notions of the sign (his notions change over the course of hiswritings) are general semiotic notions and are rarely intended to have specifically linguisticuses. Peirce has layers upon layers of signs in his philosophy. In AUG, the notion of the sign isconsiderably simpler. The notion of the sign of: meaning of relation in AUG is much closer toSaussure's notions of signifier and signifie, but is differently developed. Both Shaumyan andSaussure reject the notion that language is a stock of labels stuck onto different aspects ofreality. The notions of sign in AUG and in Saussure are not identical. For AUG, sign and meaningare not primitive notions; sign of and meaning of are the primitives. In other words, there are no

4signs or meanings outside of a bilateral relation. Saussure sees signs as "real objects", whilesaying that signs and their relations are what linguists study Saussure (1966:102). The sign of:meaning of and meaning of: sign of relations are not symmetrical. A sign communicates ameaning but a meaning does not communicate a sign. Saussure has two descriptions of thesign: one as a unilateral notion and another as a bilateral unit. AUG eliminates Saussuresbilateral sign as unnecessary and redescribes the notion of the unilateral sign. Shaumyan(1987:16-17) AUG's notion of the sign must be understood broadly. While many linguistic signsare sound sequences, AUG does not limit signs to sound sequences. Indeed, the absence of asound sequence can be a sign. AUG permits what it calls zero signs. Signs can have any level ofcomplexity. Due to the central importance of the sign for AUG and the innate complexity oflinguistic signs, the delimitation of linguistic signs is a fundamental problem that presents greatdifficulties... Shaumyan (1987:4)The implications of the sign of: meaning of relation is substantial. Several of these implicationshave been developed into principles. One important principle is the Principle of theDifferentiation of Signs:

If two signs are different, they must be differentiated by different sequences of phonemes.

Shaumyan (1987:5)Phonemes do not necessarily have meanings but all phonemes have a differentiating (diacritic)function. The Principle of the Differentiation of Signs says that if two signs are different, theymust be distinguished from each other by different phonemic patterns2. While signs can besequences of phonemes, a phoneme is not a sign. A sign is an entity (understood broadly) thathas meaning, i.e., a sign is an entity that can be part of a sign of: meaning of relation. Strictlyspeaking, AUG is not concerned with either signs or meanings in an abstract sense. AUG isconcerned only with sign of: meaning of relations Shaumyan and Sypniewski (1995:1). Animportant implication of AUGs concern with the sign of: meaning of relation will be discussedlater in the section on Semiotic Relevance. The reader must understand the importance of thediacritic nature of the sign. A sign is not just a marker or a flag for a meaning. A signdistinguishes the meaning to which it is related from all other meanings. AUG does not place anysignificance on the degree to which one meaning is different from other meanings. What isimportant is that one meaning can be differentiated from other meanings through signs.

Language has two distinct semiotic strata, the system of signs and the system ofdiacritics. Phonology studies the diacritic system and grammar studies the sign system. Thenotion of two semiotic strata requires AUG to describe two levels of grammar: the universal, orgenotype level, and the language specific, or phenotype level. Genotype grammar is unique toAUG. The greatest portion of Shaumyan (1987) is taken up with a description of genotypegrammar.

Sequencing

Sequencing, i.e., the order in which signs are produced, is an obvious and fundamentallyimportant part of language. Sequencing is a powerful method for the construction anddevelopment of new signs, words, and sentences. Sequencing pervades AUG but is not aseparately developed notion.

2 For two phonemes to be different, i.e., for them to beconsidered to be two different phonemes, there must besomething about each phoneme that distinguishes it from theother.

5Rule Use

AUG sees language as a rule-based sign system. Rules are useful for eliminating or limitingerrors, for example, in the selection of usable sequences of sound. Language is selective andredundant. No language uses all possible sequences of sounds, letters, or words. The totalnumber of possible sequences is enormous and beyond our capacity to memorize. We userules to help construct acceptable sequences and reject unacceptable ones. Since there arefewer rules than sequences, it is easier to remember the rules than to remember all of theacceptable sequences. A grammar is a description of the set of linguistic rules used by aparticular language community.

Different rules may produce different acceptable sequences with identical meanings.For example, sentences can be either active or passive and still express the same meaning.The ability to create equivalent but different constructions, called the polytectonic property oflanguage, is an important, inherent quality of natural language. Artificial languages aremonotechtonic and produce only unique constructions.

Structure

The fact that sentences have structure accounts for language's ability to develop apotentially infinite number of sentences. The structure of a sentence is a description of theinterrelationship of the parts of the sentence. Sentence structure is the network of syntagmaticrelations between its parts and paradigmatic relations between each part and all otherexpressions that can be substituted for it Shaumyan (1987:8). Syntagmatic relations are therelations between parts of the sentence; paradigmatic relations are relations between wordsthat can be substituted for each other in a sentence. A complete statement of the structure of asentence requires the mention of all its syntagmatic and paradigmatic relations.

Words and sequences of phonemes have a structure similar in many ways to that ofsentences. For example, any two roots that can acceptably share a common suffix or any twosuffixes that can be admissibly attached to a single root are examples of syntagmatic andparadigmatic relations (respectively) of words and phonemic sequences. Contrast is a wordused to designate syntagmatic relations and opposition is used for the designation ofparadigmatic relations.

Hierarchical Stratification

Language is functionally stratified. AUG identifies a large number of functional strata. Sixfunctions stand out:

Sounds, which have no linguistic function, embody phonemes and linguistic units; Phonemes have a differentiational (or diacritical) function; Morphemes signify root or non-root concepts; Parts of speech have symbolic functions; Sentence parts have a syntactic function; and Sentences are units of communication.

AUG also notes functions like deixis and several communication functions: a representational,a vocative, and an expressive function for sentences.

Hierarchical stratification is central to AUG. A main concern of AUG is to discover the lawsthat describe and control the functional levels of language.

6Semiotic Relevance

The Principle of Semiotic Relevance is implied by the sign of: meaning of relation inlanguage. The Principle states that the only semiotically relevant distinctions between meaningsare those which cause a difference in signs, and vice versa. When a language community seesa difference between two aspects of reality, it will express that difference by using differentsigns; we can also say that a language community sees an significant difference between twoaspects of reality if that community refers to those aspects of reality with different signs. Thesign of: meaning of relation is conventional, i.e., it is the product of a society Shaumyan(1987:11-12); see also Shaumyan and Sypniewski (1995). Two similar signs that do not reflectdifferent meanings are variants of the same sign; two meanings, though conceptually similar, thatproduce different signs are different meanings.

A relevant distinction in one language may not be relevant in another. What may beimportant semiotically may not be important extrasemiotically, and vice versa. There is atension between the semiotic and extrasemiotic aspects of language that is resolved in aspeech act. A speech act transforms a semiotic aspect of meaning into the extrasemiotic, sothat the transmitted message can be properly understood by the hearer. Shaumyan (1987:12) Semiotic Relevance is empirically testable. The existence of ambiguity supports thevalidity of the Principle of Semiotic Relevance. An ambiguous sentence not only has twopossible meanings but, because of the structure and sequencing of the sentence, the heareror reader cannot determine with assurance which meaning is intended. If the Principle ofSemiotic Relevance were invalid, ambiguity would not be recognized because there would be noway to differentiate meanings3. For AUG, ambiguity is caused by the improper correlation of thedistinctions between signs and their meanings in a particular sentence.

Homonymy may be seen as providing a counter-example to the Principle of SemioticRelevance. A homonym may be seen as a single sign that represents two or more distinctmeanings. Under the Principle of Semiotic Equivalence, we expect two signs rather than one;yet, we see what appears to be one sign. AUG sees homonyms as two different signs whichshare the same form but which belong to two different sign of: meaning of relations. InShaumyan (1987), such a sign is called a polyvalent sign; in Shaumyan and Sypniewski(1995), it is referred to as a polymorphic sign. AUG rejects the notion of homonymy.

Linguistics as part of Semiotics

AUG claims that linguistics is part of semiotics because natural language is a subset of theclass of all sign systems but the class of all sign systems is broader than the class of alllanguages. Linguistics studies the natural sign system that is human language. To function as ahuman language, a sign system must be capable of expressing all of the concepts that alanguage community needs expressed. This notion, referred to as cognitive flexibility, means thatmessage transmitted by a sign system can be translated into a human language but, because ofthe richness of human language, the converse is not always possible.

As a consequence of cognitive flexibility, language must have a diacritic system to enablethe production of a potentially infinite number of signs. A sign is produced by combining

3 A sign and a meaning form a sign of: meaning of relation.If two relations are similar, we can be confused. We may notunderstand which relation is intended. The fact that we candistinguish two meanings means that there are two sign of:meaning of relations. If we could not distinguish twomeanings then there would only be one relation.

7diacritics; a sign can be seen as nothing more than a combination of diacritics. Cognitive flexibilitymakes natural language the type of system known as a "very large system" in cybernetics.Because of the richness of "very large systems", such systems cannot be completely observed orcontrolled4. The richness of very large systems is due to the very large number of distinctionsthat such a system is capable of making.

If a natural language is seen as a very large system in the cybernetic sense, weimmediately perceive a problem: the explanation of language acquisition by children. AUGhypothesizes the existence of a simpler sign system that underlies language. AUG names thissimple sign system the linguistic genotype and assumes that linguistic genotypes are common toall human languages5. This is a fundamental notion without which AUG cannot be understood.Natural languages are embodiments of linguistic genotypes. The functioning of a naturallanguage simulates the functioning of a linguistic genotype. Linguistic genotypes do not existseparately from natural languages but are "built into" all natural languages. AUG studieslinguistic genotypes, i.e., the common semiotic properties of natural languages. To put itanother way, AUG sees all human languages as functioning the same way on what AUG refers toas the genotype level. As we will see, AUG proposes that any human language operates,simultaneously, on two different levels: the phenotype level, roughly corresponding to the level ofoperation described by traditional linguistics, and the universal, genotype level.

Linguistics is frequently seen as a branch of psychology. Psychological principles are notneeded for the understanding of sign systems. While a psychological investigation of languagecan provide us with important insights, such an investigation is not necessary for a linguisticunderstanding of language. Indeed, any psychological investigation of language presumeslinguistic principles. AUG rejects the claim that linguistics is a branch of psychology.

Some Goals for Linguistic Theory

Despite the substantial differences between languages, all languages have significantsimilarities. For example, every language differentiates between the functions of predicates andterms in a sentence. Language differences are not unlimited. Take word order; because of thenature of human speech, word order can occur in one of a limited number of patterns. Thereare constraints on the forms that natural language can take; an example of a constraint onlanguage is the aforementioned Principle of Semiotic Relevance.

A linguistic theory must have several goals:

1. the essential semiotic properties of natural language must be defined and their consequencesmust be explored;

2. it must account for linguistic facts of languages and equate them to the basic semioticproperties of all natural language;

3. it must create typologies and grammars for languages; and

4. a linguistic theory must be able to justify its abstractions.

4 There is a similar idea in the growing field of non-lineardynamics.5 Shaumyan (1987) does not discuss language acquisition verymuch but it is possible to argue that what children (or otherlanguage learners) acquire is the phenotype rather than thegenotype of language.

8 Much of the book consists of tracing the abstractions proposed by AUG which arebased on an examination of the consequences of the semiotic description of language.

Synchronic and Diachronic Linguistics

Synchronic facts are the syntagmatic and paradigmatic oppositions between linguisticunits existing at certain times in the history of a language; diachronic facts are correspondencesbetween two successive states of a language. AUG recognizes a paradoxical relation betweenthe synchronic and diachronic facts of a language. Diachronic facts both account for synchronicfacts and are irrelevant to them. Synchronic facts are logically independent of diachronicfacts. Synchrony is both logically prior to diachrony and more fundamental to the study oflanguage. Synchrony also shows that language has the two semiotic strata that we havepreviously seen: phonology and grammar, with the term grammar taken in its broadest sense.

Languages often have dialects which can be divided into four types, two of which aresynchronic and two diachronic. Shaumyan (1987) only considers one type : a monochronic,monotopic linguistic system in which time and space are excluded.

AUG and Generative Grammar

There are several obvious differences between generative grammar, as proposed by NoamChomsky, and AUG. Generative grammar is not a sign system; AUG is. While there are rules inChomsky's system, rules are external to language; in AUG, they are an integral part oflanguage. In AUG, grammar cannot be understood separately from meaning. The sign of:meaning of relation - the basic linguistic unit - prohibits grammar from being separated frommeaning. Chomsky uncouples grammar and meaning, a basic element of his linguistic ideas.According to Shaumyan, Chomsky has confused the notions of lexical and grammaticalmeaning. Chomsky's famous Colorless green ideas sleep furiously is, for Chomsky,grammatically correct but meaningless. For AUG, the sentence may be lexically meaninglessbut it is grammatically meaningful. Grammatical meanings are categorical and functionalmeanings, the most general meanings that a linguistic unit can have. Unless we understand thegrammatical meanings of the linguistic units in a sentence, we cannot even tell whether anexpression is meaningless or not.

Grammatical meanings are morphological and syntactic categories Shaumyan (1987:25)In Shaumyan and Sypniewski (1995:2-8) the notion of lexical and grammatical meaningsexpands beyond that in the book. The distinction between lexical and grammatical meaningsis theory neutral. The Principle of Obligatoriness must be understood before thenotion of grammatical meaning can be understood. There are a closed set of notions in everylanguage which are needed to express the language users' view of reality; an example is agrammatical meaning which expresses time, e.g., tense. In some languages, like Russian, timeis expressed grammatically; in Indonesian, the time perspective is expressed by the lexicalmeanings of language. The grammatical and lexical meanings of some words are coordinated,e.g., cat has a lexical meaning which refers to an object and a grammatical meaning - term -which also refers to an object. The word rotation, on the other hand, has uncoordinatedlexical and grammatical meanings. The grammatical meaning of rotation - term - refers to anobject but its lexical meaning refers to a process or continuing event. Grammatical meanings can be either inflectional or derivational. Derivational meaningsare structural meanings, e.g. the suffix -er. Inflectional meanings divide into two classes:functional meanings and specifying meanings. The functional meaning of a morphemedescribes the syntactic function of a word, e.g., predicate, modifier. A specifying meaning is ameaning belonging to particular types of words, e.g., predicates have specifying meanings fortense. The notions of grammatical and lexical meanings are not synonymous with syntaxeme

9and semanteme as used in other linguistic theories. There is another opposition related tolexical and grammatical meanings: syntactic and semantic meanings. Using this terminology,semantic meaning covers lexical meanings and all grammatical meanings except strictlysyntactic ones. Many linguists consider syntactic meanings to be merely functions. AUGdisputes this. Syntactic meanings are highly abstract; they denote connections between words.

Generative grammar sees syntax as a form of lexical meaning. AUG considers this to bea confusion between grammatical and lexical meanings. There is one sense in which thedistinction between semantic and syntactic meanings provides a significant insight. Semanticmeanings are directly connected to the world; syntactic meanings are only indirectly related tothe world. Seeing syntax as the relation between words in different positions in a sentenceand semantics as the relations between words which may fit into a particular place in asentence, we can consider syntax to be a set of "horizontal" relations and semantics to be aset of "vertical" relations.

AUG does not claim that the grammatical and lexical meanings are distinct. Blendinggrammatical and lexical meanings forms a heterogeneous whole. Shaumyan and Sypniewski(1995:6). Grammatical and lexical meanings are part of an opposition grammatical meaning:lexical meaning, which is frequently ignored in other linguistic theories. Shaumyan andSypniewski (1995:7) Grammatical meanings are not directly accessible. Lexical meaningsare the meanings of word stems; grammatical meanings are the meanings of inflectionalmorphemes, prepositions, conjunctions, and other devices such as word order. Shaumyan andSypniewski (1995:7) Grammatical meanings need not be "words" nor do all words need tohave lexical meanings, as can be seen from words like prepositions. Words like articles andprepositions must have meanings (at least grammatical meanings) because they are signs, butthey need not have lexical meanings. Shaumyan (1987:25) To return to the differences between generative grammar and AUG, we note that generativegrammar is a mathematical formalism that promises a set of rules for generating "correct"sentences and only "correct" sentences for a particular grammar. Even granting the claim that therules so generated actually work as the theory requires, the mere fact that a mathematicalformalism creates working rules does not imply that the language which it claims to describe workslike the mathematics it uses or the rules that it generates. AUG aims at an explanation oflinguistic phenomena and not merely a simulation of them. Generative grammar is not intendedto be explanatory. AUG does not reject the use of mathematical or logical tools in thedescription of language; an examination of Chapter 3 of Shaumyan (1987) will dispel any suchnotion. AUG claims that it is not enough to merely create "correct" sentences. We need to knowwhy sentences are "correct". In order to be satisfactory, any linguistic theory must not distort orignore linguistic facts. AUG claims that Generative Transformational Grammar cannot meet thesegoals. Shaumyan (1987:23-31)Part 2 - Phonology

In AUG, the main goals of phonology are :

the strict separation of functional and physical levels of sounds used in language; and

the study of the interrelationship between the two layers of phonology.

Shaumyan sees a dangerous gap between phonology and experimental phonology;phonologists often ignore experimental data and experimental phonologists are often uncertain ofthe validity of phonologists' theoretical explanations of their data. Shaumyan believes that a studyof the interplay of the functional and physical levels of language sounds is capable of restoringcommunication between these two camps. AUG's two phonological levels are at odds with thephonology of generative grammar. After its origin around 1959, generative phonology replaced a

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defective multilevel phonology. AUG does not propose a return to the older defective phonologybut rather to rehabilitate some of its more useful ideas and an to advance new ideas.

Phonemes are diacritics that are part of the diacritic of: sign of relation. The initial description ofthe phoneme in Shaumyan (1987:32) does not equate a phoneme with a sound but, rather, witha linguistic entity which distinguishes signs. Although speech can be seen as strings ofsegmented phonemes, speech is a actually a continuous flow. The central problem of phonologyis the solution of the problem of speech sound identity. Speech continuity creates an intrinsicvariability in speech sounds. AUG has a principle, called the Principle of Speech SoundVariability, which states that speech sounds are environmentally modified during speech acts.Different language groups classify similar sets of sounds in different ways (phonic relativity).Phonic relativity creates the problem of the identity of speech sounds.

In order to address the problem of speech sound identity, Shaumyan uses the Principle ofDifferentiation of Signs which requires that linguistic signs be differentiated by different diacriticsequences. The position of sounds helps us in our examination. When comparing groups ofsounds, it is important to note the position of phonemes with regard to other phonemes in eachset. Each set of phonemes has two distinctive features: concrete distinctive oppositions andconcrete phonemes. When ordering each set by some positional relation, the relations that orderthe sets of sounds in each position are known as the concrete distinctive relations. The terms(phonemes) in these relations are known as concrete phonemes. Concrete phonemes are notmerely physical sounds; concrete distinctive oppositions semiotically function to distinguish one signfrom other signs. Concrete distinctive oppositions have important properties called concretedistinctive features. A set of concrete phonemes ordered by a concrete distinctive oppositionis called a paradigmatic class of concrete phonemes. Shaumyan (1987:32-35) With these new concepts in mind, the problem of speech sound identity can be rephrased as:What determines the identity of concrete phonemes that occur in different positions? Shaumyan(1987:35) Because AUG sees phonemes as relational entities, the question can be rephrased as:What determines the identity of the structure (isomorphism) of paradigmatic classes of concretephonemes? Shaumyan (1987:35) AUG postulates the Law of Phonemic Identity: Two paradigmatic classes of concrete phonemes Ki and Kj are identical if their relationalstructure can be put into a one-one correspondence, so that to each concrete phoneme x of Kithere corresponds a concrete phoneme y of Kj, and to each concrete distinctive opposition r of Kithere corresponds a distinctive opposition s of Kj, and vice versa. There is a one-onecorrespondence between concrete phonemes x and y, and between concrete distinctive oppositionsr and s, if the difference between x and y and between r and s is reducible solely to the effect ofpositional variation. Shaumyan (1987:35) AUG resolves the problem of speech sound identity by splitting the concept of speech soundsinto two distinct parts: speech sound proper and the concrete phoneme. Speech sounds can bedistinguished by physical analysis; concrete phonemes are distinguished by the Law ofPhonemic Identity. Although concrete phonemes are physical entities, the distinction betweenconcrete phonemes is not based on their physical characteristics. Shaumyan (1987:36) The Law ofPhonemic Identity is capable of predicting the behavior of phonemes in situations where differentconcrete phonemes are identical with respect to their physical properties, and, ... where twoidentical concrete phonemes are completely different with respect to their physical properties.Shaumyan (1987:36-39) The notion of phonetic features becomes split into two segments:functionally identical phonetic features (concrete distinctive features) and physically identicalphonetic features (phonetic features proper). Classes of functionally identical concrete phonemesand classes of physically identical sounds are logically independent of each other. Shaumyan(1987:39) The following terminology will be used in this section:

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An abstract phoneme is a class of concrete phonemes.

An abstract distinctive opposition is a class of concrete distinctive oppositions.

An abstract speech sound or sound type is a class of concrete speech sounds.

An abstract phonetic feature is a class of concrete phonetic features.

Phonology has two levels: physical and functional. For convenience, Shaumyan follows themathematician Markov in using identifying idealizations. He creates abstract phonemes. Simply put,an abstract phoneme is the result of a convention which says that if an identical phoneme occursmore than once in a word, it will be convenient to treat the phonemes as multiple occurrences ofone phoneme rather than as separate phonemes. In titillate, the phoneme t occurs three timesrather than there being three separate phonemes t, for example.

When compared, the definition of phoneme as a diacritic and the definition of phoneme as aconcrete speech sound that functions as a term in distinctive opposition are complementarydefinitions. Speech sounds have a dual nature. The functional and physical identities of a speechsound are complementary but mutually exclusive ideas. AUG refers to the sound/diacriticcombination rather than just the sound as a phoneme. The concepts of sound and phoneme are twodifferent levels of abstraction and are not related by class inclusion or membership. Shaumyandraws an analogy to waves and particles in physics to explain the relationship between sounds anddiacritics. He calls this type of relation a "centaur" relation. AUG requires that the functional andphysical levels be strictly distinguished at all times.

Speech Flow Segmentation

Speech sounds segment both physically and functionally; the segments are independent ofeach other. Shaumyan cites different opinions about whether linguistic criteria make anydifference in speech sound segmentation. Speakers segment speech into discrete units, aphenomenon Shaumyan calls the physical segmentation of the speech flow. The aim of AUG'sphonology is to determine the basis of functional segmentation.

The single concrete phoneme is the minimal part of a linguistic sign Shaumyan (1987:43)but a minimal part of a linguistic sign may consist of several sounds. On the other hand, two soundsmay consist of one or two concrete phonemes. Shaumyan (1987:44) Two considerations enterinto the functional interpretation of two signs. First, a sequence of two sounds can be eithercohesive or noncohesive. If cohesive, the sequence is a single concrete phoneme; if noncohesive,the sequence is two concrete phonemes. Second, in a sequence of two sounds, if either sound canbe replaced by another sound or by a "zero" sound, then the sequence represents two phonemes;otherwise, the sequence is a single phoneme. Sometimes a sequence of two phonemes mayappear in a position like a single phoneme that is an element of the sequence. In such cases, thesingle phoneme can be seen as the "realization" of the two-phoneme sequence. Shaumyan(1987:45-46)A Return to the Problems of Functional Identity

Some sounds cannot acceptably follow certain other sounds while other related sounds can.Shaumyan uses the English language example of b, d, and g following s. None of these voicedstops can acceptably follow s in an English word, but the unvoiced stops p, t, and k can. Thequestion arises: when a sound x cannot appear in position p1 but a related sound y can appear inposition p1, can x be said to be functionally equivalent to y in positions where both can occur? Ifwe remember that AUG concerns itself with relations rather than "objects", we can anticipatethe answer. Functional equivalence depends on whether x and y can be members of a binaryrelation x:y. In the case of the sounds mentioned above, the phonological oppositions p:b. t:d, or g:k

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do not exist because p, t, and k can appear after s but b, d, and g cannot. P, t, and k after s mergewith s into one phoneme; b, d, and g cannot. Such mergers are called neutralizations; the productof a neutralization is called an archiphoneme.

Phonological Antinomies

AUG recognized that there are certain antinomies in phonology at least as early asShaumyan (1968). Antinomies of the paradigmatic and syntagmatic identification of phonemesare created by the consequences of two assumptions:

Speech sounds are discrete physical elements.

Speech sounds function as diacritics; they distinguish signs according to the Principle ofSemiotic Relevance.

The first assumption predicts that speech sounds will not be identical but the secondassumption permits identical sounds. The first assumption suggests that two speech soundscannot constitute one phoneme, while the second assumption permits just such a merger.Furthermore, a third theoretical antimony emerges. If we assume that the role of phonemes is todistinguish signs and we further assume that phonemes are acoustic elements, we get whatShaumyan calls the antinomy of transposition, which concerns the transposition of types of signs.The first assumption permits us to substitute one type of sign for another, e.g., a graphic sign for aacoustic sign. We say that the "medium" of the sign makes no difference to a sign of: meaning ofrelation. However, if the second assumption is valid, that phonemes are acoustic signs, once wetranspose a phoneme into, say, written form, we destroy the phoneme and, hence, the sign. Notingthe consequence of accepting the second assumption, we might be tempted to reject the firstassumption as invalid. AUG's response is that we are able to distinguish between the phoneme andits acoustic substance. A phoneme is, so to speak, the value of an acoustic entity, not the entityitself. Shaumyan (1987:50-54) AUG asserts that linguistic ideas can, and do operate according to a notion akin to NielsBohr's Complementarity Principle in physics. Shaumyan (1987:54-55) Complementarity is anotion that several descriptions of a single phenomenon can be simultaneously maintained andcan prove useful, even if they appear to be contradictory; rather than being contradictory, inreality, they are complementary, so that if they are taken together, we get a better and, perhaps,more complete description of some aspect of reality than any single description providesindividually. As physics has shown, some descriptions of an aspect of reality, when seen fromdifferent points of view, can appear to contradict other descriptions of the same reality, despite thefact that both descriptions are accurate. The key to understanding a complementarity principle is tonote that many phenomena, like language and quantum level physics, are so complex that anobserver can only observe and describe a portion of the phenomenon at any given time. Theobserver has a "point of view" which can and often does change with the observation.Although neither traditional Western logic nor linguistic theory takes "point of view" into account,quantum mechanics, which has been called the most successful scientific theory in humanhistory, could not function without due consideration being give to the point of view of theobserver and the effects of the observation on the observed. Shaumyan proposes a similarconsideration in linguistic theory. Incorporating the notion of complementarity to linguistics is oneof AUG's major advances over traditional linguistic theory. The notion of complementarity allows usto study language without understating its inherent complexity. While it is beyond the scope ofthis monograph to proceed further, it should be noted that AUG is strongly influenced by quantummechanics. See, e.g., Shaumyan's references to Bohr in a discussion of phonologicalinvestigation Shaumyan (1987:58-60) and his development of the linguistic notion of"superposition", which we will see later, originally a quantum mechanical notion developed byDirac.

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Shaumyan acknowledges that his three antinomies are not without their critics. The readeris referred to Shaumyan (1987:55-58) for a review of some criticisms and Shaumyan's refutationof them. None of the criticisms, even if accepted, does damage to AUG. Shaumyan also reviewssome alternate theories of the phoneme, especially that of Trubetzkoy, and shows where, inseveral places, the theories are inconsistent. Shaumyan (1987:61-66)Phonological Syntagmatics

Every language strictly constrains sequences of phonemes; sequences that would beacceptable in one language are not acceptable in another. Sequences have structure due to thecomposition and arrangement of their individual phonemes. The minimal sequential phonologicalelement is the syllable; other, larger phonological elements also exist. Shaumyan usesTrubetzkoy's term culminative function to describe the role of accent in words. The culminativefunction uses accent to distinguish words from each other. Each word has one accent; in speech,we can count the number of words in the speech flow by counting accents. The accent is placed ona particular syllable, the accented syllable becoming the "center" of the word, with all other syllablesbecoming "satellites" of it. Shaumyan (1987:66) While Trubetzkoy noticed the culminative function with regards to accent, AUG sees a similarfunction within syllables. A syllable is centered around its vowel feature. One segment of thesyllable becomes central, while the other segments are satellites of it. AUG sees an analogybetween the phonological functions of words and syllables. Shaumyan (1987:66-67) Theseobservations lead to the conclusion, at odds with some phonological theory, that vowels andconsonants cannot appear in the same position and that only vowels can be opposed to vowels, andconsonants to consonants. Shaumyan offers several proofs of this conjecture Shaumyan(1987:67-69) Stress has another function besides the culminative function. Stress can distinguish signs.Usually stress does not have this secondary function, but we should be alert for those occasionswhen stress does. Shaumyan (1987:68-69) A syllable and a phonological word are not the same. A phonological word can be a sign; asyllable cannot. Syllables do not have meaning (syllables cannot enter a sign of: meaning ofrelation) by themselves. Monosyllabic words are not exceptions or counter-examples to this rule.Monosyllables only function as words because they have meaning; they do not have meaningbecause they are words. As an example, language speakers of Vietnamese (a highly monosyllabiclanguage) take monosyllables and make them into sign of: meaning of relations. Unless and untilthat is done, a monosyllable is not a sign.

AUG observes that syllables are universal phonological units, i.e., every known languageuses syllables. However, the phonological word, which requires a stress as a component, is notuniversal. In some languages, the number of stresses in a particular speech flow does notsignal the number of words in the flow. Shaumyan gives examples from French and German. Inthe latter case, in which compounding words is a major method of vocabulary expansion, acompound word may have several stresses. The largest phonological unit is a phonologicalsentence with intonation. Intonation has both a culminative function and a distinctive function.Shaumyan (1987:69-70) From the analysis briefly described above, Shaumyan derives four laws applicable to alllanguages:

The Law of Phonological OppositionNo language can have an opposition of vowels and consonants. Vowels oppose vowels;consonants oppose consonants.

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The Law of Phonological ContrastVowels and consonants contrast (have syntagmatic relations).The Law of Phonological FunctionsThe culminative function is obligatory only for vowels; the distinctive function is obligatory forconsonants and optional for vowels.

The Law of Minimal VocalismThe minimal vocalism is either two vowels with a distinctive function or one vowel with no distinctivefunction.

These laws are not inductive; they are the products of an analysis of the semiotic propertiesof language. Shaumyan (1987:70-71) The Law of Minimal Vocalism implies that there can be languages with a monovocalicphonological system. The Law of Phonological Opposition says that only vowels can opposevowels, and consonants . This law presupposes at least two phonemes. Any vocalism that has adistinctive function must, therefore, have at least two phonemes. The culminative function is basedon contrast and, according to the Law of Phonological Contrast, vowels and consonants cancontrast. Therefore, a minimal vocalism, limited to contrast, must be confined to one vowel.Shaumyan (1987:70-71) Shaumyan cites some controversial examples of languages, e.g., fromthe Northern Caucasus, which fit this description. A fuller exploration is promised in another book.Shaumyan (1987:71)The Structure of Syllables

A syllable has three parts: an onset, a nucleus, and a coda. The combined nucleus and codaare called the core. Vowels are the phonemes that function as the nucleus, the irreducible portion,of the syllable. A syllable without a coda is "open"; a syllable with a coda is "closed". In somelanguages, closed syllables occur either rarely or not at all, but no language has syllables that donot have onsets. There is a basic opposition - onset:core. Every language must have this oppositionbut not every language must have the opposition nucleus:coda. These two oppositions form ahierarchy. If the analysis of a syllable is seen as a constituency tree, the opposition onset:core is themost basic branch point on a tree, with the opposition nucleus:coda branching from the core.

There is an intimate relationship between the quantity or intonation of a syllable and its core.The quantity of a syllable is fixed by the core. We see that long nucleus = short nucleus + codaShaumyan (1987:72-73) In some languages which have cores consisting of only short vowels,stresses must pass to other vowels since short vowels cannot be stressed. These are the so-called"light" syllables. A "heavy" syllable consists of either a long vowel, two short vowels, a short vowelplus a consonant, or some combination of these three.

A basic problem for phonology is the definition of the syllable boundary. Shaumyanintroduces the notion of the interlude to address this problem. Shaumyan (1987:73) Theinterlude is a string of one or more consonants between two vowels. An interlude may be eitherunary or binary. A binary interlude has two components: the left part (the coda of the precedingsyllable) and the right part (the onset of the succeeding syllable). A unary interlude is a binaryinterlude without the right component. Of the two possible components of an interlude, the right partis the most important since the left part presumes that there is an onset (all languages haveonsets) but an onset does not presume a coda (not all languages have codas). AUG assumes that there is a relationship between syllable boundaries and word structure.Ideally, the same constraints on the sequencing at the beginning of a word should also operate onthe beginning of a syllable and the same constraints that operate on the sequencing at the end of

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the word should operate at the end of the syllable. AUG defines the following basic principles fordetermining syllabic boundary:

The interlude constitutes the onset of the next syllable, unless the preceding syllable cannotbe open because of vowel sequencing. In this case, the necessary number of consonants mustbe detached from the onset and added to the coda of the preceding syllable.

If the interlude cannot occur at the beginning of a word, as many consonants as necessary aredetached in order to make the interlude acceptably appear in a word-initial position. Thedetached consonants are attached to the coda of the preceding word. Shaumyan(1987:73-74)

Shaumyan acknowledges that his proposed definition of vowels and consonants is notgenerally accepted. Some linguists dispute the universality of Shaumyan's phonological definitions,specifically the observation that sometimes consonants act as syllabic nuclei, with vowels as theirsatellites. While agreeing that one and the same phoneme may function sometimes as asyllable nucleus and sometimes as a nonsyllabic phoneme in the same language Shaumyan(1987:75), Shaumyan points to the primary and secondary functions of a phoneme to support hisposition. The primary function of vowels is to serve as syllabic nuclei and, secondarily, theyfunction as consonants; the primary function of consonants is to serve as satellites of vowels andtheir secondary function is to serve as syllabic nuclei.

The notion of primary and secondary functions of phonemes is based on observations of the"range" (the distribution of phonemes within a syllable) of phonemes. The range of phonemes isnot related to the statistical notion of frequency but is solely defined by its distributional possibilities.Shaumyan (1987:75) If the range of a phoneme is greater when it serves as a syllabic nucleus, theprimary function of that phoneme is to serve as a syllabic nucleus; when its range is greater when itserves as a satellite, then that is its primary function.

Clements and Keyser introduced the notion of the "extrasyllabic consonant" to describewhat they saw as a consonant which is not part of any syllable, e.g., the initial consonant in theEnglish pronunciation of Gdansk. Shaumyan sympathizes with the motivation for the creationof the "extrasyllabic consonant" but views it as unnecessary. The g in Gdansk exercises itssecondary function and becomes a syllabic nucleus; to ease pronunciation an ultra-short schwa isadded. Shaumyan (1987:76-77) The notion of "extrasyllabic consonant" is an ad hoc solution to aparticular problem; the notions of primary and secondary functions of a phoneme are generaland arise from an analysis of the structure of a syllable. Furthermore, extrasyllabic consonantsmake otherwise regular linguistic units irregular while the notion of primary and secondaryfunctions of the phoneme do not. The latter notions, which are more general than the notion ofextrasyllabic consonants, explain the phenomena in a more precise way and arise from a semioticanalysis of language, are, therefore, to be preferred to the notions developed by Clements andKeyser. Shaumyan (1987:77)Prosodic Features

Prosodic features are elements in a speech flow whose duration differs from the duration ofphonemes. Usually, prosodic features have longer duration than phonemes, as can be seen insyllables or phonological words that are longer than a single phoneme. However, prosodicfeatures are sometimes shorter than phonemes, as in the case of a syllabic nucleus splitting into twoconsecutive units (morae). Prosodic features can be divided into two groups: accentual andnonaccentual prosodic features.

Stress can be either bound or free. Stress is bound in a given language if it always appearsin one and the same place or if its place is strictly determined by the phonemic structure of aword. Stress is said to be free if it can occupy various places in a word, independent of the

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phonemic structure of the word. Free stress has both a culminative function and a worddifferentiation function.

Depending on the manner of setting off a stressed syllable, AUG recognizes several typesof stress:

(a) strong, or dynamic, stress (the stressed syllable is set off by greater tenseness of its articulation);(b) quantitative stress (the stressed syllable is set off by increased lengthening of the articulationof the vowel); and(c) tonal, or musical, stress (the stressed syllable is set off by a change in the tone pitch).

Shaumyan (1987:78)

Nonaccentual prosodic features are relevant to more than one syllable. Their only purpose isword differentiation; they have no culminative function.

A mora is the smallest speech segment that can carry a prosodic feature.

In AUG, prosodic features are relational entities independent of definite phonic substance.When differentiating prosodic and nonprosodic elements of speech, We do not differentiatebetween fundamentally different substances. Prosodic and nonprosodic elements are simplyspeech elements that are susceptible to different types of analysis. At this point, Shaumyanreintroduces the Principle of the Transposition of Phonological Structure:

Any phonological structure can be transposed from one phonic substance to another as long asthe phonological relations characterizing this structure remain intact.

Shaumyan (1987:79)The Principle of the Transposition of Phonological Structure predicts that a phonic substancethat may be a prosodic feature in one language may not be a prosodic feature in anotherlanguage. Shaumyan gives the example of the glottal stop which is a phoneme in Arabic, is adistinctive feature characterizing glottalized phonemes in a few American Indian languages, and isneither a phoneme nor a distinctive feature in Lettish or Danish, but is an accent, that is to say, aprosodic feature.

Comparison with Generative Phonology

The phonological component of generative-transformational grammar consists of two levels:systematic phonemics and phonetics. The systematic phonemic level converts representations ofunderlying phonemic forms into phonetics. Systematic phonemics roughly corresponds to themorphophonemic level of non-transformational grammar, and systematic phonetics roughlycorresponds to phonetics in non-transformational grammar. Generative transformationalgrammar rejects the notion of the existence of a phonemic level and replaces it with generativephonology. Shaumyan examines some of the claims of Morris Halle using the Principle of SemioticRelevance. Halle claims that the morphophonemic (phonemic) level is unnecessary and can bedispensed with. Halle says that the existence of the phonemic level is based on the following:

A phonological description must include instructions for inferring (deriving) the properphonological representation of any speech event, without recourse to information not contained inthe physical signal.

Shaumyan (1987:81)

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Halle notes that the procedures referred to in what he calls Condition 3a (the quote above) are"essentially analytical". Halle says that Condition 3a creates an unscientific classificationmethod; ...it sets up a distinction between phonemes and morphophonemes for the sole reasonthat the former can be identified on the basis of acoustic information alone, whereas the latterrequire other information as well. Since it has never been shown that phonology differs from othersciences in such a way as to warrant such a deviation in classification procedure (the opposite - thatphonology is a science just like all others - is usually asserted), Condition 3a is an uncalled-forcomplication and should be dispensed with.

Shaumyan generally agrees with this criticism. However, after examining the example ofRussian phonology cited by Halle, Shaumyan shows that it was incorrectly interpreted. ReanalyzingHalle's example raises the question of the correct basis for phonological theory. A comparison ofthe goals of phonology in AUG and generative transformational grammar is instructive.Phonology, in AUG, studies a system of distinctive oppositions. The starting point for this study isthe phonemic level as an ideal system of distinctive oppositions whose properties aredetermined by the Principle of Semiotic Relevance. Shaumyan (1987:83) This ideal system ofdistinctive oppositions is not based on analytical procedures; it is the theoretical basis from whichpossible systems are deduced, i.e., it is a theoretical systems used for the purpose ofunderstanding real world systems. Since generative phonology studies a system of alternations,it must base its theory on the morphophonemic level of language.

Shaumyan sees this important difference between AUG and generative phonology: a systemof distinctive oppositions is inherent in all languages but a system of alternations is not. A system ofalternations is important to languages that have such a system but not all languages do. It isimportant to keep one feature of AUG always in mind: it is intended as a universal theory. AUG isa theory of linguistic features which underlie all languages and which is intended to explain theworkings of all languages by constructing a set of basic, universal, theoretical models. Universalityis a goal of all aspects of AUG. While other theories purport to be applicable to all languages,their emphasis on universality is not as central as it is with AUG. A consequence of the quest foruniversality is the level of generality of AUG's description of linguistic features. Shaumyannotes that generative phonology would have a difficult time defining the notion of "distinctiveoppositions" but that the notion of "alternations" is not significantly difficult to define in AUG'sterms (Alternations are nothing other than a subset of distinctive oppositions that hold betweenallomorphs of morphemes. Shaumyan (1987:84)). Alternations are founded on the synchronic structure of the phonetic level of language.Shaumyan concludes that this poses a constraint on the type of rules that can be developed. TheCondition of Synchronic Motivations reads:

No rules should be formulated in phonetic terms if they do not correspond to synchronicprocesses in the structure of the phonemic level.

Shaumyan (1987:84)This condition prevents the substitution of diachrony for synchrony in phonological studies.

Shaumyan creates an integrated phonological theory with two basic goals. The first is thestudy of systems of distinctive oppositions as "autonomous objects" and the study of systems ofalternations as objects partially subordinated to systems of distinctive oppositions. Distinctiveoppositions are autonomous because they are independent of systems of alternations. Anintegrated phonological theory also has a methodological goal of studying the constraints onphonological model making. We have already seen an important constraint: the Condition ofSynchronic Motivation. Shaumyan notes three others:

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[t]he strict separation of functional and physical equivalence of sounds and acousticfeatures;

functional and physical segmentation of the speech flow;

phonetically and nonphonetically conditioned alternations

Shaumyan (1987:86)Shaumyan's brief suggestions about phonological model building will be omitted, except to notethat none of the suggestions are dogmatic. Perhaps because of its universal outlook, AUG does notinsist that its goals be met by following the "one true path".

By ignoring language's nature as a sign system, generative phonology has confusedsynchrony and diachrony as well as confusing the phonemic level with the morphophonemic andphonetic levels of language. Shaumyan examines the claim that the Ordering Hypothesis (that rulesare ordered) is "one of the best supported assumptions of linguistic theory". He disagrees with thisassertion. While agreeing that language is hierarchically structured (indeed, hierarchicalstratification is one of the bases of AUG), Shaumyan points out that the Ordering Hypothesis refersto an extrinsic and, therefore, arbitrary ordering rather than an intrinsic and natural ordering. Theerroneous claim for the Ordering Hypothesis is a result of the formal design of generativetransformational grammar. Generative transformational grammar is capable of producingphonological objects; generative transformational grammar assumes that, since it can producephonological objects with mathematical procedures, the mathematics used accuratelydescribes the way that language works. Shaumyan correctly notes that The generative model isbased on logical necessity, but logical necessity does not necessarily conform to empiricalnecessity. Shaumyan (1987:87) and again that the mathematical consistency of a theory does not,ipso facto, mean that the theory is a correct description of reality. Shaumyan (1987:92) Thegenerative notion of linguistic competence is the unfortunate conflation of synchrony anddiachrony. Shaumyan reviews a number of examples from Chomsky's works and shows theconfusion between synchrony and diachrony that he claims for generative phonology. Shaumyan(1987:88-92)Part Three - Genotype Grammar

Genotype grammar is a notion unique to AUG; the uniqueness of genotype grammar is aconsequence of AUG's special concern for universality. Genotype grammar is a grammar of a"universal" language. By this, I mean that genotype grammar is not intended to be thegrammatical theory of any specific language but, instead, is intended to be a grammaticaldescription of the common features of all languages.

A universal description of language imposes certain requirements on its underlyingformalism. Obviously, the formalism of a genotype grammar cannot be based on the formaldescription of any particular language. To do so would create two significant problems:

we would have to justify the selection of the language on which we decide to base ourformalism.

the act of selection suggests that the language chosen as the basis for a universal formalism issomehow "better" for the job than other languages; i.e., that some language might bemore "universal" than others (somehow, the chosen language has more "universal" featuresthan others or that a "universal" language description should be somehow like the chosenlanguage) or that some languages are somehow "deviant" or not as "universal" as others.AUG avoids these problems by creating a formalism that is not based on the grammar of anyspecific language or on the formalism of any other linguistic theory.

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Genotype grammar is one of the two types of grammar discussed in AUG. As mentioned,genotype grammar is a universal grammar. AUG also posits a phenotype grammar, specific to eachlanguage. The genotype level of a language can be understood as the functional level of alanguage while the phenotype level can be understood as the syntagmatic level of the language. Acomplete description of any language is a description of both its genotype and phenotype levels.

Basic Terms

The minimal sign is the morpheme. A combination of morphemes is called a syntagm. Morphemes, words, and groups of words are called syntagmatic units.

A language has functional units. Functional units are observed when we view languageas an instrument of communication.

The basic functional unit is the sentence. The purpose of the sentence is to transmitmessages from sender to receiver. An importance consequence of viewing language as aninstrument of communication is that unless a word or group of words functions as a unit ofcommunication, i.e., a sentence, the word or group of words does not transmit a message.

After the sentence, the most basic functional element is the predicate. The predicate functionsas the "representative" of the sentence; the predicate is the irreducible minimum componentof a sentence.

It may be objected that English does not permit a declarative sentence to consist of only averb. An English declarative sentence must have both a predicate and a subject. Shaumyanresponds that this correct observation is an observation of the phenotype level of English. Thereare rules that require English to have sentences that meet this description, but these rules donot apply to all languages. In no language can a sentence lack a predicate. Recall that thegenotype level of language is the universal level; the fact that the predicate is indispensable tosentences in all languages is the basis of AUG's claim for the centrality of the predicate. The readershould not think that AUG says that the well-known fact that English requires properly formeddeclarative sentences to have subject terms is an incorrect observation. AUG simply says thatsuch an rule does not apply to all languages, another well-known fact. Rather than declaring thatlanguages which are not consistent with a syntax similar to Englishs to be somehow deviant ornonnormative, AUG places this rule on the phenotype (language specific) level rather than on thegenotype (universal) level.

The term predicate and other terms we will see (primary term, secondary term, tertiaryterm, term modifier, and predicate modifier) are intentionally chosen to be neutral terms of art.Shaumyan (1992:8) Each of these terms must be understood as referring to functions on thegenotype level of language and not on the phenotype level. When we say something like "thepredicate is indispensable to all languages", the reader should understand this to mean "thepredicate is indispensable to the description of the genotype grammar of all languages".

Another important functional element is the term. The term is a complement to the predicate.The predicate denotes a situation; the term designates a participant in the situation denoted bythe predicate. Predicates and terms can be modified by predicate modifiers and term modifiers.

These four, predicates, terms, predicate modifiers, and term modifiers, are not the onlyfunctional units that inhabit a genotype grammar, but they are the only four described in any detailby Shaumyan (1987). The four types of functional elements are not simply "preferred terms" forverb, noun, adverb, and adjective. The words verb, noun, adjective, and adverb are the names ofsyntagmatic units. Syntagmatic and functional units belong to different levels of the description of

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language. Syntagmatic and functional elements do not have a one-to-one correspondence. As wewill see, functional units can be composed of groups of words as well as single words. A functionalunit can also be as small as a single morpheme. The latter observation leads to the distinctionbetween two types of syntactic connections:

syntactic connections between functional units and

syntactic connections between units that realize functional units, that is, syntactic connectionsbetween syntagmatic units.

Shaumyan (1987:97)Shaumyan cites considerable confusion between these two types of syntactic connections incurrent linguistic literature, agreement and government being examples. Shaumyan (1987:97) Abasic observation of AUG is that the syntactic structure of a sentence is independent of itssyntagmatic representation. This observation leads directly to the observation that grammar has twolevels (or that language has two levels of grammar).

The genotype and phenotype levels of language can be described as follows:

Genotype grammar comprises functional units - predicates, terms, modifiers - and abstractoperator-operand relations between these units. Phenotype grammar comprises syntagmatic units -morphemes and words - and connections between them in terms of linear order and theirmorphological properties.

Shaumyan (1987:97)The terms genotype and phenotype are consciously borrowed from biology to emphasize therelation between the two linguistic levels. Just as genes are invariant with respect to differentphenotypes, the rules of the genotype level are invariant with respect to different phenotypes(individual languages). Acceptance of the two level description of language puts us on the road tothe solution of the basic question of linguistic theory... What factors contribute to the similaritiesand differences between natural languages? Shaumyan (1987:97) Shaumyan uses passivization as a demonstration of the importance of seeking languageinvariants, i.e., genotype rules and descriptions, for linguistic phenomena. Generativetransformational grammar sees the change from an active form of a sentence to a passive form as atransformation. While there are many proposals for exactly how passivization should be viewed ingenerative transformational grammar, all proposals basically come down to transforming a sentencein the form NP1 V NP2 to NP2 V(pass) NP1. We can see that this is so for English sentences butcan we maintain such a rule universally? Shaumyan says no. The generative transformationalrule just mentioned relies on the linear order of English as its basis. In Malagasy, an activesentence is in the form V NP2 NP1 (with NP1 being the subject and NP2 being the object); in itspassive form, it becomes V(pass) NP1 NP2. In many languages, such as Russian, word order isirrelevant for passive transformations. Russian active and passive sentences can have thesame word order. Russian active and passive forms depend on the case markings of its terms.

A universal rule for passivization cannot be stated in terms of word order, as generativetransformational grammar suggests. Word order and the system of case markings are languagedependent; in the terminology of AUG, they exist on the phenotype level. To create a universalpassivization rule, we must examine the functional units on the genotype level. For our purposeshere, we can see the predicate as a binary relation involving an actor and a patient. Passivization isthe conversion of this binary relation. Conversion is an operation that creates the converse of arelation R, which we shall call R'. R' holds between X and Y iff R holds between Y and X. A passivepredicate is the converse of an active predicate. In an active sentence, the primary term is theagent and the secondary term is the patient; in a passive sentence, the primary term is the patient

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and the secondary term is the agent. Primary and secondary terms will be described later, but, fornow, the reader should keep in mind that the names primary and secondary do not imply linearposition or a fixed word order.

The rule that the passive is the converse of the active is universal, i.e., the rule is not languagedependent. One of the hallmarks of a universal rule is that it is predictive. In three examplelanguages, English, Malagasy, and Russian, the passivization rule correctly predicts the outcomefor each language. The predictiveness of universal rules makes AUG testable in a way thatgenerative transformational grammar is not. Another result predicted by our rule is that, since ourrule is an operation on the predicate, we expect the predicate to be modified in some way. We notethat the predicates in our examples are morphologically marked to indicate their passive form.Shaumyan (1987:97-101)Some Basic Notions of Genotype Grammar

Communication, i.e., a language act, has three functions, expressive, vocative, andrepresentational functions, depending whether the language act is focused on the sender,receiver, or some subject matter external to the language act, respectively.

Shaumyan concentrates on the representational function of language acts.

The Principle of Representational Relevance is a postulate that describes some of the basicelements of communication that are considered by AUG. The Principle states that, after weremove everything in the language that is irrelevant to the representational function of thecommunication, we find that there are only three types of linguistic expressions remaining: the"names" of objects, the "names" of situations, and methods for constructing either or both typesof "names". Shaumyan (1987:101) I have drawn attention to the word "name" because it is bothof central importance and easily misunderstood.

AUG calls the "name" for an "object" a term and the "name" for a "situation" a sentence.

AUG calls any means for creating terms or sentences operators.

A term should not be misunderstood to be a noun. While a term can be a noun, a term canalso be what is traditionally referred to as a noun phrase.

For example, car, the car, the big car, and the big, yellow car are all examples of a term. Each isthe "name" of an object, here only coincidentally a tangible object in the real world. Each exampleterm can refer to the exact same object or to different objects; nonetheless, each example is botha "name" and a term. It should be noted that "term" is the "name" of the linguistic function of eachof the language examples just given. Like a sentence, a term can be thought of as being constructed of parts. Unlike generativetransformational grammar, AUG does not recognize a term, once constructed, as still beingcomposed of parts, except for convenience. Generative transformational grammar, which isbased on first order logic, sees a phrase like the big, yellow car as actually being the + big + yellow+ car, in short, a unit composed of arbitrary parts. AUG, which is based on second order logic, seesthe big, yellow car, once constructed, as a single functional unit. This distinction, which at firstseems to be subtle and, perhaps, not worth noticing, has significant implications. Some areexplored in Shaumyan (1987). Operators permeate genotype grammar.

An operator is any kind of linguistic device that acts on one or more expressions called itsoperands to form an expression called its resultant. Shaumyan (1987:101)

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Operators must operate on something; an operator cannot function without operands. An operatormay have one or more operands.

An operator with n operands is referred to as an n-place operator.

Operators should not be confused with verbs. While a verb is a type of operator, it is far from beingthe only type of operator in genotype grammar.

Any kind of linguistic device can be an operator; to take a few examples, morphemes,intonation, and even zero signs can be operators.

Shaumyan does not simply graft second order logic on top of linguistics and declare the resultto be a new linguistic theory. He uses the techniques of second order logic to explore and explainlinguistic phenomena and, from the results of his explorations, develops a new linguistic theory(AUG). For instance, Shaumyan notes that logic treats all operands as being equally connected toits operator. In short, no operand receives any preference in treatment by the operator. Linguisticsshows that language does not quite work this way, that language shows degrees of connectednessbetween operands and their operators. Here are some examples:

A transitive verb (an two-place operator) is more closely connected to its direct object (secondaryterm) than with its subject (primary term).

The combination of a transitive verb and its object is equivalent to an intransitive verb. One canreplace the other without loss of meaning, e.g., to dine can replace to eat dinner and viceversa.

This last observation explains certain types of ambiguity. Nouns derived from intransitive verbs are"oriented" toward the subjects of the actions described and nouns derived from transitive verbs areoriented towards the objects of their actions. Some verbs, e.g. shoot, can be used bothintransitively and transitively. When such a verb becomes a noun (shooting), it creates theambiguous situation of whether the action it describes is oriented towards its subject or object (theshooting of the hunters). Shaumyan notes that the orientation of nouns derived from transitiveverbs towards the object of the actions described is a universal tendency. It has been shown, first by Moses Schnfinkel and later by Haskell Curry, that an act ofcombination involving an n-place operator is actually a series of one place combinations repeated ntimes with the operator using different operands each time. Shaumyan sees the implication of thislogical observation for linguistics. Take the sentence The hunter killed the bear Shaumyan(1987:103). In this sentence, killed is a two place operator, the hunter is the primary term, and thebear is the secondary term. Rather than applying the operator killed to all its terms at once, AUGapplies it first to the secondary term, as the previous observations suggest it should. The resultant atthe first step of the application gives us two units: a one-place predicate combined with itssecondary term ((killed the bear)), a unit now equivalent to an intransitive verb, and the primary term(the hunter). The new, one place predicate is now applied to the primary term. The resultant isthe sentence (also called an s-type or, simply, s): ((killed the bear) the hunter). The process whichwe have just run through is called an application, hence the name of Shaumyan's theory,Applicative Universal Grammar.

The Applicative Principle formally defines the process which we have just seen:An n-place operator can always be represented as a one-place operator that yields an (n-1)-placeoperator as its resultant.

Shaumyan (1987:103)

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Keep in mind that the results of applying an operator to an operand is another operator; second-order logic discusses operations on functions which yield other functions. Even a sentence is anoperator; it is a zero-place operator, i.e., an operator which cannot operate any further (there isnothing left to operate on). The sentence is the basic unit of communication in all languages.

Here are the definitions of a one, two, and three place predicate, and primary, secondary, andtertiary terms.

Definition 1. If X is an operator that acts on a term Y to form a sentence Z, then X is a one-placepredicate and Y is a primary term.

Definition 2. If X is an operator that acts on a term Y to form a one-place predicate Z, then X is atwo-place predicate and Y is a secondary term.

Definition 3. If X is an operator that acts on a term Y to form a two-place predicate Z, then X is athree-place predicate and Y is a tertiary term.

Shaumyan (1987:103-104)Notice that the definitions above are not the definitions of operator but of predicate. The notion ofpredicate roughly corresponds to the traditional notion of verb, but is not be restricted to thetraditional notion. The phrase that acts on in the above definitions can also be read as combineswith. When an n-place predicate combines with a term, it produces an (n-1)-place predicate that isthe linguistic structure of the predicate combined with the linguistic structure of the n-ary term. It isthis combination which is referred to as the (n-1)-place predicate and which operates on the n-aryterm.

Application can be described in applicative tree diagrams. The interested reader shouldrefer to Shaumyan (1987:104) for examples.Constituency

Operators and operands are interconnected by constituency and dependency relations. Anoperator and its operand are related as parts to a whole (constituency relation) with its resultant. Anoperator and operand exist in a dependency relation; either the operator or the operand can be thehead of such a relation with the other being the dependent. Both constituency and dependencynetworks exist simultaneously.

If A is an operator and B is its operand, C is the resultant of applying A to B. A and B are calledthe immediate constituents of C. In general, C can have an arbitrary number of constituents.

Constituents are not defined in terms of word order. Constituents need not be linearly adjacentto each other, as in generative transformational grammar.

If C is the resultant of applying the operator A to the operand B, then either A is the head of adependency relation with B as its dependent, or vice versa.

If C belongs to the same linguistic category as B, then B is the head and A is thedependent, and vice versa.

If B is the head and A the dependent, then A is called the modifier of the head; otherwise, A iscalled the complement of the head. Shaumyan (1987:106-107).

Shaumyan gives this example. There are several operator : operand combinations in the sentenceBill bought new books. Applying new (an operator) to books (its operand), we get (new books). New

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is the modifier of books because new books is in the same category as books, both being terms.When we apply bought to (new books), we get (bought (new books)). Since (bought (newbooks)) and (new books) are in different linguistic categories, (bought (new books)) being apredicate, bought is the head of a dependency relation with (new books) being its complement.Once again, applying (bought (new books)) to Bill, we get another dependency relation with (bought(new books)) as its head and Bill as its complement because the resultant of applying (bought (newbooks)) to Bill is ((bought (new books)) Bill), which is a sentence or s-type. The notions of head and dependent in AUG are more general than in current dependencygrammar. Dependency grammar cannot describe dependency between functional units whileAUG can. AUG does not view dependency as a primitive concept. Dependency grammar cannotdefine dependency; AUG, using the notion of application, can. AUG sees no conflict betweenconstituency and dependency but, rather, sees these notions as complementary. Shaumyan doesnot see constituency as being superior to dependency or vice versa; neither can be dispensedwith. Both constituency and dependency, in AUG, are relations between operators, operands,and resultants.

Sentence Structure

Before discussing AUG's conception of sentence structure, we need to mention certain basicnotions. In order to understand sentence structure from a genotype point of view, we must realizethat discussions about the details of the genotype stratum are not discussions of syntax. Thegenotype stratum is composed of functional units. These functional units are universal andirreducible. A comment such as Neither words nor combinations of words belong to syntax properShaumyan (1987:109) may, at first, seem startling, but it must be understood as a comment basedon the two-strata view of language. The genotype stratum does not have syntax; the phenotypelevel of language has syntax. The genotype stratum is composed of abstract types that alllanguages have. The phenotype level of a language is a syntagmatic realization of theuniversal genotype level peculiar to that language. In order to emphasize this distinction, Shaumyancoined the word syntaxeme for functional units.

Predicate Frames

A predicate frame is a combination of a predicate and a number of operands (terms) which willresult in a sentence. The smallest predicate frame consists of a predicate and a primary term.Shaumyan does not use the word subject but prefers primary term. The primary term isprivileged; the name refers to a participant whose role, whether active or passive, is emphasizedby its choice as the primary term Shaumyan (1987:110) Shaumyan refers to this role as a "pivot".The importance of the primary term is reflected in the linguistic fact that it alone among terms isindispensable to a sentence.

Traditionally, sentences are seen as an expansion of the basic sentence that consists of only apredicate. In AUG, the sentence is a reduction of structures based on the predicate :primary term relation. We will see the reason for this claim when we review the Principle ofMaximal Differentiation. AUG recognizes that a predicate, by itself, can form a completesentence. In this case, the predicate : primary term relation is dispensed with. In some languages,e.g., Latin, sentences without explicit primary terms are quite common.

A two-place predicate plus a secondary term and a one-place predicate without a term aresyntactically equivalent. A three-place predicate with a term is syntactically equivalent to a two-place predicate without a term. Tertiary and secondary terms are more closely connected to theirpredicates than primary terms. Sentences which contain more than one term must be constructedby incorporating terms into predicates. Note that the notion of predicate and term combinationis not a theoretical construct but results from observation of linguistic facts. Shaumyan gives

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examples of predicate/verb combinations collapsing into simple predicates, e.g., form a circleround collapses to encircle Shaumyan (1987:112) Predicates and terms can be operated on by modifiers. Taking the case of a term, weobserve that the elementary form of a term is a noun and the elementary form of a term modifier isan adjective. Term modifiers are not limited to adjectives; the role of term modifier can be taken byother words or groups of words. AUG recognizes that words have primary and secondaryfunctions. The primary function of an adjective is to be a term modifier; the primary function of averb is to be a predicate but one of its secondary functions is to be a term modifier. Even asentence has primary and secondary functions. Its primary