Semantics and Computational Semantics
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This document discusses computational semantics, examining how meaning is represented and understood in language technology. It emphasizes the importance of semantics in enabling intelligent applications to interpret human language correctly, employing techniques such as propositional and predicate logic. The document also explores various methods for semantic representation, reasoning, and the challenges involved in natural language processing.
Semantics and Computational Semantics
- 1. 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]fil.uu.se Department of Linguis(cs and Philology Uppsala University, Uppsala, Sweden Spring 2016 Lecture 2: Computational Semantics 1
- 2. 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$cs hJp://www.let.rug.nl/bos/pubs/BlackburnBos2003Theoria.pdf Some slides are borrowed from / inspired by: • Manning C.: Computa(onal Seman(cs, CS224N Stanford University hJp://web.stanford.edu/class/cs224n/handouts/Computa(onal %20Seman(cs.pdf • Dragomir Radev: Introduc(on to NLP, Coursera Lecture 2: Computational Semantics 2
- 3. Outline • Representa(on and Seman(cs • Computa(on and Composi(onal Seman(cs – Logic – Unifica(on • Conclusions Lecture 2: Computational Semantics 3
- 4. What is Seman(cs? Lecture 2: Computational Semantics 4
- 5. Generally speaking… seman(cs is the study of meaning that is used for understanding human expressions through language • Seman&cs is the study of meaning: accounts for links between words and the world. • Seman(cs is the study of how meaning is conveyed through signs and language. – Denota(ons are the literal or primary meanings of words. – Connota(ons are ideas or feelings that a word invokes for a person in addi(on to its literal or primary meaning. • Seman(cs focuses on the rela(on between signifiers (like words, phrases, signs, and symbols) and what they stand for, ie their denota(ons (concepts) and connota(ons (seman(c analysis). Lecture 2: Computational Semantics 5
- 6. Comput(er)-‐a(onal Seman(cs • Seman$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. Lecture 2: Computational Semantics 6
- 7. 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 Lecture 2: Computational Semantics 7
- 8. Why do we need ”meaning” in Language Technology? • The short answer is: because ”intelligent” applica(ons must ”understand” in order to act. Lecture 2: Computational Semantics 8
- 9. Ex 1: Google -‐ What is the capital of Sweden? • Answer: Lecture 2: Computational Semantics 9
- 10. Ex 2: Siri -‐ Which countries does the Danube river flows through? Lecture 2: Computational Semantics 10
- 11. 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 Lecture 2: Computational Semantics 11
- 12. 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… Lecture 2: Computational Semantics 12
- 13. 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. Lecture 2: Computational Semantics 13
- 14. 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. Lecture 2: Computational Semantics 14
- 15. REPRESENTATION AND SEMANTICS Lecture 2: Computational Semantics 15
- 16. 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 Lecture 2: Computational Semantics 16
- 17. 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 Lecture 2: Computational Semantics 17
- 18. 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". Lecture 2: Computational Semantics 18
- 19. 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. Lecture 2: Computational Semantics 19
- 20. 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) Lecture 2: Computational Semantics 20
- 21. 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 Lecture 2: Computational Semantics 21
- 22. Truth table Lecture 2: Computational Semantics 22
- 23. Proposi(onal Logic and Seman(cs Transla$ng propos$ons to Eng Seman$cs of Proposi$onal Logic Lecture 2: Computational Semantics 23
- 24. 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. Lecture 2: Computational Semantics 24
- 25. 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” Lecture 2: Computational Semantics 25
- 26. Used to represent • Objects – Mar(n the cat • Rela(ons – Mar(n and Moses are brothers • Func(ons – Mar(n’s age Lecture 2: Computational Semantics 26
- 27. 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 Lecture 2: Computational Semantics 27
- 28. FOL elements (long version) Formula → AtomicFormula or Formula Connec(ve Formula or Quan(fier Variable Formula or ¬ Formula (Formula): Lecture 2: Computational Semantics 28
- 29. FOL’s most important feature: quan(fiers à generaliza(on Lecture 2: Computational Semantics 29 To ace a test = to get a very high score on a test
- 30. Proper(es of Predicate Logic • Pros – Composi(onal – Declara(ve • Cons – Limited expressive power – Represents facts Lecture 2: Computational Semantics 30
- 31. 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 Lecture 2: Computational Semantics 31
- 32. Stages of Seman(c Parsing • Input – Sentence • Syntac(c Analysis – Syntac(c structure • Seman(c Analysis – Seman(c representa(on Lecture 2: Computational Semantics 32
- 33. 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 Lecture 2: Computational Semantics 33
- 34. Example • Input – Javier likes pizza • Output – like(Javier, pizza) Lecture 2: Computational Semantics 34 Associate a semantic expression with each node
- 35. 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 Lecture 2: Computational Semantics 35
- 36. What about ”kick the bucket”? • What happens when the meaning of single words does not lead to the meaning of the whole? Lecture 2: Computational Semantics 36
- 37. COMPUTATION AND COMPOSITIONAL SEMANTICS Lecture 2: Computational Semantics 37
- 38. 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. Lecture 2: Computational Semantics 38
- 39. 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. Lecture 2: Computational Semantics 39
- 40. 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. Lecture 2: Computational Semantics 40
- 41. 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? Lecture 2: Computational Semantics 41
- 42. CONCLUSIONS Lecture 2: Computational Semantics 42
- 43. 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 Lecture 2: Computational Semantics 43
- 44. In this course… • We review research about different aspects of word meaning that are needed for LT-‐based applica(ons. Lecture 2: Computational Semantics 44
- 45. 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 (???) Lecture 2: Computational Semantics 45
- 46. Reminder: Glossary Entries • Which concepts are the most salient in this lecture? • Start crea(ng your Glossary now… Lecture 2: Computational Semantics 46
- 47. The End Lecture 2: Computational Semantics 47