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Seman&c Analysis in Language Technology http://stp.lingfil.uu.se/~santinim/sais/2016/sais_2016.htm

Semantics and

Computational Semantics

Marina San(ni [email protected]

Department of Linguis(cs and Philology Uppsala University, Uppsala, Sweden

Spring 2016

Lecture 2: Computational Semantics 1

Acknowledgements The content of these slides is mostly based on the following chapter: •  Stone M. (In Press) Seman$cs and computa$onal seman$cs To appear in

Paul Dekker and Maria Aloni, eds., Cambridge Handbook of Formal Seman(cs. hJps://www.cs.rutgers.edu/~mdstone/pubs/compsem13.pdf

•  Blackburn P. and Bos J. (2003) Computa$onal Seman$cs hJp://www.let.rug.nl/bos/pubs/BlackburnBos2003Theoria.pdf

Some slides are borrowed from / inspired by: •  Manning C.: Computa(onal Seman(cs, CS224N Stanford University

hJp://web.stanford.edu/class/cs224n/handouts/Computa(onal%20Seman(cs.pdf

•  Dragomir Radev: Introduc(on to NLP, Coursera


Outline

•  Representa(on and Seman(cs •  Computa(on and Composi(onal Seman(cs – Logic – Unifica(on

•  Conclusions


What is Seman(cs?


Generally speaking… seman(cs is the study of meaning that is used for understanding human expressions through

language

•  Seman&cs is the study of meaning: accounts for links between words and the world.

•  Seman(cs is the study of how meaning is conveyed through signs and language. –  Denota(ons are the literal or primary meanings of words. –  Connota(ons are ideas or feelings that a word invokes for a person in addi(on to its literal or primary meaning.

•  Seman(cs focuses on the rela(on between signifiers (like words, phrases, signs, and symbols) and what they stand for, ie their denota(ons (concepts) and connota(ons (seman(c analysis).


Comput(er)-‐a(onal Seman(cs

•  Seman$cs is the study of meaning in language. •  Computer science is the study of precise descrip(ons of finite processes;

•  Thus, computa(onal seman(cs embraces any project that approaches the phenomenon of meaning by way of tasks that can be performed by following definite sets of mechanical instruc(ons.


We can start by saying that…

”The aim of computa(onal seman(cs is to find techniques for automa(cally construc&ng seman&c representa&ons for expressions of human language, representa(ons that be used to perform inference. ” Blackburn and Bos (2003).

Inference = reasoning


Why do we need ”meaning” in Language Technology?

•  The short answer is: because ”intelligent” applica(ons must ”understand” in order to act.


Ex 1: Google -‐ What is the capital of Sweden?

•  Answer:


Ex 2: Siri -‐ Which countries does the Danube river flows through?


Ex 3: Facebook Graph Search Facebook Graph Search was a seman$c search engine that was introduced by Facebook in March 2013. It was designed to give answers to user natural language queries rather than a list of links.” Examples: "Friends who Like Star Wars and Harry Po@er” "photos of my friends taken at Na&onal Parks" hJps://en.wikipedia.org/wiki/Facebook_Graph_Search


Understanding Meaning

If an agent (eg. a robot) hears a sentence and act accordingly, the agent is said to understand the sentence: Example: Leave the book on the table Understanding may involve inference: Which book? Which table? So, understanding may involve some kind of reasoning…


NLP/LT and Seman(cs •  Not all LT-‐based applica(ons require seman(cs. –  Ex: taggers, parsers, etc.

•  Much can be done with shallow seman(cs. –  Ex: word sense disambigua(on, etc.

•  For more complex tasks (more ”intelligent” tasks”) seman(c reasoning is needed. –  Ex: QAnswering, Info Extrac(on, Ontology Crea(on, etc.


Tradi(onally… …reasoning is done by using some kind of logic… A tradi(onal approach is to use FOL (first order logic) to ”formalize” meaning (see Formal Seman(cs Theories). … before start studying how seman(cs is used in Language Technology-‐based applica(ons, let’s summarise how seman(cs has been brought into computer science and ar(ficial intelligence.


REPRESENTATION AND SEMANTICS


Proper(es of Meaning in Logic •  Verifiability

–  Can a statement be verified against a knowledge base (KB) –  Example: does my cat Mar(n have whiskers?

•  Unambiguousness –  Give me the book –  Which book?

•  Canonical form (standard/abstract form of an expression) •  Expressiveness

–  Can the formalism express temporal rela(ons, beliefs, …? –  Is it domain-‐independent?

•  Inference


Represen(ng Meaning

•  A tradi(onal approach to meaning is to –  use proposi(onal logic – predicate/first order logic (FOL) – use theorem proving (inference) to determine whether a statement entails another


Proposi(onal Logic : proposi(ons are represented by leJers

•  In proposi(onal logic, we use leJers to symbolize en(re proposi(ons.

•  Proposi(ons are statements of the form "x is y" where x is a subject and y is a predicate.

•  For example, "Socrates is a Man" is a proposi(on and might be represented in proposi(onal logic as "S".


True and False •  Proposi(onal Logic studies proposi(ons, whether they are true or false. •  A sentence might contain several proposi(ons that are linked together by

logical connec(ves.

•  Logical connec(ves are found in natural languages. In English for example, some examples are "and" (conjunc(on), "or" (disjunc(on), "not” (nega(on) and "if" (but only when used to denote material condi(onal).

•  Ex (wikipedia): simple inference within the scope of proposi(onal logic: •  Premise 1: If it's raining then it's cloudy. •  Premise 2: It's raining. •  Conclusion: It's cloudy.

Both premises and the conclusion are proposi(ons. The premises are taken for granted and then with the applica(on of modus ponens (an inference rule) the conclusion follows.


Syntax of Proposi(onal Logic •  The simplest type of logic – If S is a sentence, ¬S is a sentence (nega(on) – If S1 and S2 are sentences, S1 ∧ S2 is a sentence (conjunc(on) – If S1 and S2 are sentences, S1 ∨ S2 is a sentence (disjunc(on) – If S1 and S2 are sentences, S1 ⇒ S2 is a sentence (implica(on) – If S1 and S2 are sentences, S1 ⇔ S2 is a sentence(bicondi(onal)


Proposi(onal Logic and Natural Language

Operator Precedence ¬ (highest) = nega(on ∧ = conjunc(on ∨ = disjunc(on ⇒ = implica(on ⇔ (lowest) = bicondi(onal* *A bicondi(onal statement is defined to be true whenever both parts have the same truth value.

Logic and Language A = Today is a holiday. B = We are going to the park. A ⇒ B A ∧ ¬ B ¬ A ⇒ B ¬ B ⇒ A B ⇒ A


Truth table


Proposi(onal Logic and Seman(cs

Transla$ng propos$ons to Eng Seman$cs of Proposi$onal Logic


Proposi(onal logic vs FOL/Predicate Logic

•  Proposi(onal logic (also called senten(al logic) is logic that includes sentence leJers (A,B,C … ) and logical connec(ves, but not quan(fiers. The seman(cs of proposi(onal logic uses truth assignments to the leJers to determine whether a compound proposi(onal sentence is true.

•  Predicate logic is usually used as a synonym for first-‐order logic. Syntac(cally, first-‐order logic has the same connec(ves as proposi(onal logic, but it also has variables for individual objects, quan(fiers, symbols for func(ons, and symbols for rela(ons.

•  Its seman(cs includes a domain of discourse for the variables and quan(fiers to range over, along with interpreta(ons of the rela(on and func(on symbols.


Predicate Logic: more expressive than Proposi(onal Logic

•  In predicate logic, we symbolize subject and predicate separately.

•  The important difference is that you can use predicate logic to say something about a set of objects.

•  By introducing the universal quan(fier ("∀"), the existen(al quan(fier ("∃") and variables ("x", "y" or "z"), we can use predicate logic to represent thing like: –  "Everything is green" as "∀Gx” ” –  Something is blue" as "∃Bx”


Used to represent

•  Objects – Mar(n the cat •  Rela(ons – Mar(n and Moses are brothers •  Func(ons – Mar(n’s age


FOL elements (short version)

•  Constant •  Variables •  Predicates •  Boolean connec(ves •  Quan(fiers •  Brackets and comma to group the symbols together

•  Ex: A woman crosses Sunset Boulevard


FOL elements (long version)

Formula → AtomicFormula or Formula Connec(ve Formula or Quan(fier Variable Formula or ¬ Formula (Formula):


FOL’s most important feature: quan(fiers à generaliza(on


To ace a test = to get a very high score on a test

Proper(es of Predicate Logic

•  Pros – Composi(onal – Declara(ve

•  Cons – Limited expressive power – Represents facts


Lambda calculus à Variable subs(tu(on

Useful for expressing computa(on by way of variable binding and subs(tu(on. Variables are just names that are bound as arguments. Lambda calculus is important in programming language theory. Example – inc(x) = λx x+1 – then inc(4) = (λx x+1)(4) = 5 Example – add(x,y) = λx,λy(x+y) – then add(3,4) = (λx,λy(x+y))(3)(4)= (λy 3+y)(4) =3+4 = 12


Stages of Seman(c Parsing

•  Input – Sentence

•  Syntac(c Analysis –  Syntac(c structure

•  Seman(c Analysis – Seman(c representa(on


Composi(onal Seman(cs

•  Add seman(c aJachments to syntac(c rules •  Composi(onal seman(cs – Parse the sentence syntac(cally – Associate some seman(cs to each word – Combine the seman(cs of words and non terminals recursively

– Un(l the root of the sentence


Example •  Input –  Javier likes pizza

•  Output –  like(Javier, pizza)


Associate a semantic expression with each node

Seman(c Parsing

•  Conver(ng natural language to a logical form – e.g., executable code for a specific applica(on –  Example:

•  Airline reserva(ons •  Geographical query systems


What about ”kick the bucket”?

•  What happens when the meaning of single words does not lead to the meaning of the whole?


COMPUTATION AND COMPOSITIONAL SEMANTICS


Unifica(on Grammar •  Unifica(on grammar is a formalism that derives seman(c representa(ons by accumula(ng constraints in tandem with a syntac(c deriva(on.

•  The constraints take the form of equa(ons between terms which may contain variables.

•  The formalism gets its name from the process, unifica$on, which determines values for variables to solve the equa(ons.


Example: ”everybody walks”

The meaning representa(on of ∀x.walks(x) is assembled as the solu(on to a set of constraints and not through the func(on–argument maninupula(on of the lambda calculus.


More flexibility •  Lambda-‐calculus techniques expect each element in a meaning

representa(on to be specified exactly once.

•  Unifica(on: we model sentence meaning as the solu(on to a set of equa(ons à we might find elements of meaning that are simultaneously determined by mul(ple equa(ons, and elements of meaning that are lev unconstrained and must be resolved by context.

•  Constraint techniques offer new ways to analyze idioms and mul(-‐word expressions. Each cons(tuent can not only specify its own meaning but can impose a constraint on the meaning of the whole.


Limita(ons

•  Composi(onal seman(cs (any formalisms) gives us representa(ons that capture aspects of the logical structure of meaning.

•  But: what specific en((es and concepts does a sentence describe, and what specific claim does it make about them?


CONCLUSIONS


Basically…

•  We need to (e together: – Grammar (grammar and composi(onal meaning is not enough)

– Speaker’s kowledge about the wolrd – PaBerns of use à unique insights given by large corpora of linguis$c evidence


In this course…

•  We review research about different aspects of word meaning that are needed for LT-‐based applica(ons.


How is *meaning* handled in Seman(c-‐Based LT-‐Applica(ons

•  Seman(c Role Labelling/Predicate-‐Argument Structure (???)

•  Sen(ment Analysis (???) •  Word sense disambigua(on (???) •  Informa(on extrac(on (???) •  Ques(on Answering (???) •  Ontologies (???)


Reminder: Glossary Entries

•  Which concepts are the most salient in this lecture?

•  Start crea(ng your Glossary now…


The End


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