Semantics for Natural Languages Compositionality Desiderata for - PowerPoint PPT Presentation

Introduction Introduction Syntax and Semantics Logical Representations Logical Representations Compositionality Semantic Composition Semantic Composition Desiderata for Meaning Representation Introduction 1 Syntax and Semantics Semantics for Natural Languages Compositionality Desiderata for Meaning Representation Informatics 2A: Lecture 25 Logical Representations 2 Mirella Lapata (based on slides by BW, JL, and SA) Propositional Logic Predicate Logic School of Informatics University of Edinburgh Semantic Composition 3 Compositionality 15 November 2011 Lambda Expressions 1 / 28 2 / 28 Introduction Syntax and Semantics Introduction Syntax and Semantics Logical Representations Compositionality Logical Representations Compositionality Semantic Composition Desiderata for Meaning Representation Semantic Composition Desiderata for Meaning Representation Syntax and Semantics Syntax and Semantics Semantics is concerned with how expressions in a language map to A possible ‘meaning’ for a sentence should take account of both a world – both their the intended senses of its words and its intended syntactic analysis. denotation (literal meaning) Take the example: connotation (other associations) I made her duck When we say (in everyday usage) that a sentence is ambiguous, we usually mean it has more than one (literal) meaning. I caused her to drop and avert her head. ( duck as action) I created the duck that she owns. ( duck as individual) Some ambiguity comes from words having more than one sense, some from sentences having more than one parse tree (syntactic I cooked a/some duck for her. ( duck as mass) analysis) with respect to a grammar, and some from a property called scope . 3 / 28 4 / 28

Introduction Syntax and Semantics Introduction Syntax and Semantics Logical Representations Compositionality Logical Representations Compositionality Semantic Composition Desiderata for Meaning Representation Semantic Composition Desiderata for Meaning Representation Syntax and Semantics Compositionality Providing a semantics for a language (natural or formal) involves Compositionality : The meaning of a complex expression is a giving a systematic mapping from the structure underlying a string function of the meaning of its parts and of the rules by which they to its ‘meaning’. are combined. While the kinds of meaning conveyed by NL are generally much While formal languages are designed for compositionality, the more complex than those conveyed formal languages, they both literal meaning of NL utterances can often be derived adhere to the principle of compositionality. compositionally as well. 5 / 28 6 / 28 Introduction Syntax and Semantics Introduction Syntax and Semantics Logical Representations Compositionality Logical Representations Compositionality Semantic Composition Desiderata for Meaning Representation Semantic Composition Desiderata for Meaning Representation Desiderata for Meaning Representation Desiderata for Meaning Representation Verifiability : One must be able to use the meaning representation Unambiguous: a meaning representation should be unambiguous, of a sentence to determine whether the sentence is true with with one and only one interpretation. If a sentence is ambiguous, respect to some given model of the world. there should be a different meaning representation for each sense. Example: given an exhaustive table of ‘who loves whom’ relations Example: each interpretation of I made her duck or time flies like (a world model), the meaning of a sentence like everybody loves an arrow should have a distinct meaning representation. Mary can be established by checking it against this model. 7 / 28 8 / 28

Introduction Syntax and Semantics Introduction Syntax and Semantics Logical Representations Compositionality Logical Representations Compositionality Semantic Composition Desiderata for Meaning Representation Semantic Composition Desiderata for Meaning Representation Desiderata for Meaning Representation Desiderata for Meaning Representation Expressivity: a meaning representation should allow a wide range Canonical form: the meaning representations for sentences with of meanings to be expressed in a natural and revealing way, the same meaning should both be convertible into the same including relationships between the words in a sentence. canonical form, that shows their equivalence. Example: we want to express restrictions on the concept denoted Example: the sentence I filled the room with balloons should have by the head of a phrase: the same canonical form with I put enough balloons in the room to fill it from floor to ceiling . brown cow (How is brown related to cow ?) man who came to dinner (or man related to came to dinner ?) Relationships other than identity should be derivable by entailment and other forms of inference. walk briskly (or walk related to briskly ?) 9 / 28 10 / 28 Introduction Syntax and Semantics Introduction Propositional Logic Logical Representations Compositionality Logical Representations Predicate Logic Semantic Composition Desiderata for Meaning Representation Semantic Composition Desiderata for Meaning Representation Introduction 1 Syntax and Semantics Expressivity: a meaning representation should allow a wide range Compositionality of meanings to be expressed in a natural and revealing way, Desiderata for Meaning Representation including relationships between the words in a sentence. Logical Representations 2 Example: we want to express predicate-argument relations, i.e., the Propositional Logic participants in the event associated with the head of a phrase: Predicate Logic Fred eats lentils (NP V NP): an eating event, with Fred doing 3 Semantic Composition the eating ( agent ), and lentils being eaten ( theme ); Compositionality Fred eats lentils with a fork (NP V NP with NP): the same, Lambda Expressions but with a fork as the instrument used for eating the lentils. 11 / 28 12 / 28

Introduction Introduction Propositional Logic Propositional Logic Logical Representations Logical Representations Predicate Logic Predicate Logic Semantic Composition Semantic Composition Propositional Logic Propositional Logic Why not use propositional logic as a meaning representation system for NL? Propositional logic is one system for representation and reasoning Fred ate lentils or he ate rice. (P ∨ Q) in which expressions comprise: Fred ate lentils or John ate lentils (P ∨ R) atomic sentences (P, Q, etc.); We lose any obvious relationship between the clauses that make up complex sentences built up from atomic sentences and logical these sentences. connectives (and, or, not, implies, etc.). Everyone ate lentils. (P1 ∧ P2 ∧ P3 ∧ P4 . . . ) Someone ate lentils. (P1 ∨ P2 ∨ P3 ∨ P4 . . . ) We can’t really express either sentence. 13 / 28 14 / 28 Introduction Introduction Propositional Logic Propositional Logic Logical Representations Logical Representations Predicate Logic Predicate Logic Semantic Composition Semantic Composition Predicate Logic Constants First-order predicate logic (FOPL) is closer to being expressive enough for NL semantics. Sentences in FOPL are built up from terms made from: Constant symbols: constant and variable symbols that represent entities; Each constant symbol denotes one and only one entity: Scotland, Perth, EU, John, George W. Bush, Scotland, 2007 function symbols that allow us to indirectly specify entities; Not all entities have a constant that denotes them: predicate symbols that represent properties of entities and George W. Bush’s right knee, this pen relations that hold between entities; Several constant symbols may denote the same entity: which are combined into simple sentences (predicate-argument The Morning Star ≡ The Evening Star ≡ Venus structures) and complex sentences through: National Insurance number, Student ID, your name quantifiers ( ∀ , ∃ ) disjunction ( ∨ ) negation ( ¬ ) implication ( ⇒ ) conjunction ( ∧ ) equality (=) 15 / 28 16 / 28