Type shifting and coercion

Henriëtte de SwartNovember 2010

Basics of type theory

• Basic types: e (entity) and t (truth-value)• Call the set of well-formed types T• Syntax of types: (i) e, t T (ii) if a, b T, then <a,b> T (iii) nothing else is in T• Function application: if is of type <a,b> and

is of type a, then () is of type b.

Applications I

• Proper names (e.g. Milly) are of type e, and intransitive verbs (e.g. swim) are of type <e,t>, so ‘Milly swam’ is of type t.

• Determiners (e.g. every) are of type <<e,t>,<<e,t>,t>>, and nouns (e.g. student) are of type <e,t>, so noun phrases (e.g. every student) are of type <<e,t>,t>.

Applications II

• If a noun phrase (e.g. every student) combines with a one-place predicate (e.g. swim), the combination ‘every student swam’ is an expression of type t.

• Modifiers (e.g. blue) are of type <<e,t>,<e,t>>, and combine with nouns of type <e,t> to create another expression of type <e,t>, e.g. ‘blue coat’.

Puzzle

• Transitive verbs (e.g. invite) are of type <e,<e,t>>, and combine with proper names (e.g. Milly) to create a VP ‘invited Milly’ of type <e,t>.

• But transitive verbs can also take generalized quantifiers as objects, e.g. ‘invited every student’.

• However, generalized quantifiers are not of type e, but of type <<e,t>,t>.

• How to combine by function application?

Flexible types

• Solution 1: give determiners a flexible type, so that they can also map intransitive verbs onto one-place predicates; every is then of type <<e,<e,t>>,<e,t>> (function raising).

• Solution 2: give transitive verbs a flexible type, so that they can map generalized quantifiers onto on-eplace predicates; invite is then of type <<<e,t>,t>,<e,t>> (argument raising).

• The syntactic configuration in which an expression occurs may influence the semantic type we assign it.

• Flexible types are used to preserve function application as composition rule.

Polysemy

• Pustejosvky (1995): polysemy challenges theories of the lexicon.

• Ambiguity: word has two unrelated meanings (e.g. bank) – homonyms: two lemmas in dictionary.

• Polysemy: word has two related meanings – one lemma in dictionary.

• E.g. count-mass alternation: a. The lamb is running in the field. b. John ate lamb for dinner.

More examples of polysemy

• Container/content: (1) a. Mary broke the bottle. b. The baby finished the bottle.• Figure/ground: (2) a. The window is rotting. b. Mary crawled through the window.• Product/producer (3) a. John spilled coffee on the newspaper b. The newspaper fired the main editor.

Functional dependencies

• What is it that an adjective is modifying? (1) a. a fast boat b. a fast typist c. a fast book• What is the complement of the verb? (2) a. Mary began to read the novel. b. Mary began reading the novel. c. Mary began the novel.• How to integrate these functional

dependencies into the construction?

Polysemy and compositionality

• Meaning alternations too systematic for listing (creative use – no sense enumeration).

• Meaning alternations are a challenge for compositional semantics, which takes the meaning of words to be a fixed starting point.

• Pustejovsky’s aim: capture systematic alternations within theory of lexicon/syntax.

• Structured information for nouns, verbs in computational linguistics and AI necessary for driving inferences in commonsense language reasoning system (Hobbs et al. 1987).

Generative lexicon: ingredients

• Argument structure: number and type of logical arguments and their syntactic realization.

• Event structure (not to be discussed here)• Qualia structure: modes of explanation,

composed of formal, constitutive, telic and agentive roles

• Lexical inheritance structure: identification of how a lexical structure is related to other structures in the type lattice, and its contribution to the global organization of a lexicon.

Generative lexicon: operations

• Type coercion: where a lexical item or phrase is coerced to a semantic interpretation by a governing item in the phrase, without change of its syntactic type.

• Selective binding: where a lexical item or phrase operates specifically on the substructure of a phrase, without changing the overall type in the composition.

• Co-composition: where multiple elements within a phrase behave as functors, generating new non-lexicalized senses for the words in competition.

Argument structure

• True arguments: syntactically realized parameters of the lexical item.

(1) John arrived late.• Default arguments: parameters which

participate in the logical expression, but which are optionally expressed syntactically.

(2) John built the house out of bricks.• Shadow arguments: parameters which are

semantically incorporated into the lexical item. (3) Mary buttered her toast with an expensive butter.

Qualia structure

• Qualia structure specifies essential aspects of a word’s meaning.

• Constitutive role: the relation between an object and its constituent parts

• Formal role: that which distinguishes it within a larger domain

• Telic role: its purpose and function• Agentive role: factors involved in its origin or

“bringing it about”.

Example of qualia structure

• Qualia structure of novel• Constitutive (content): narrative• Formal (type of object): book• Telic (what is it ‘for’): reading• Agentive (how did it come about): writing

Sense in context: qualia structure

• Qualia structure helps to see where contextual information comes from:

(1) Mary began (reading) a novel. (2) John finished (smoking) the cigarette. (3) John began (drinking) his second beer.• Qualia structure enables the noun to encode

information about particular properties and activities associated with them.

• Context principle: a syntactic phrase cannot be interpreted outside of the syntactic and semantic context within which it appears.

Type-clash and coercion

• Conflict between selection requirements of governing expressions and its argument.

(1) Mary wants a beer• Complement of want: property (verb-based),

actual complement: NP. Type clash – yet, the sentence is fully grammatical and meaningful.

• Type coercion: a semantic operation that converts an argument to the type which is expected by a function, where it would otherwise result in a type error.

Function application with coercion

• Assume that each expression has available to it a set of shifting operator, called , changing its type and denotation.

• Function application with coercion: If is of type c, and is of type <a,b>, then,

(i) If type c=a, then () is of type b. (ii) If there is a such that () results in

an expression of type a, then (()) is of type b.

(iii) Otherwise a type error is produced.

True complement coercion

• John began a book• Begin: event structure: e1 = transition, e2 =

transition, e1 t e2

argstructure: arg1 =x:human, arg2 = e2• Book: Argstructure: arg1 = x:info, arg2 = y:physobj Qualia structure:

Formal = hold(x,y)Telic = read(e,w,x,y)Agent = write(e’,v,x,y)

• John [began [Cevent [a book]]]

Modification with qualia structure I

• Adjectives like fast are event predicates, modifying some aspect of the head noun.

• Which aspect that is depends on the event-related interpretation associated with the qualia structure of the noun.

(1) a. a fast boat: fast [Cevent [boat]] (move)

b. a fast typist: fast [Cevent [typist]] (type)

c. a fast book: fast [Cevent [book]] (read)

Modification with qualia structure I

• Other modifiers make reference to the formal role of the noun:

(2) a. a red boat b. a male typist c. a French book