1CMSC 723: Intro toComputational LinguisticsNovember 24, 2004Lecture 12: Lexical SemanticsBonnie Dorr Christof MonzMeaning So far, we have focused on the structure oflanguage, not on what things mean We have seen that words have differentmeaning, depending on the context in whichthey are used Every day language tasks that require somesemantic processing: Answering an essay question on an exam Deciding what to order at a restaurant by reading amenu Realizing you’ve been insultedMeaning (continued) meaning representations arerepresentations that link linguistic formsto knowledge of the world We are going to cover: What is the meaning of a word How can we represent the meaning What formalisms can be used• Meaning representation languagesWhat Can Serve as a MeaningRepresentation? Anything that serves the core practicalpurposes of a program that is doingsemantic processing What is a Meaning RepresentationLanguage? What is Semantic Analysis?2Requirements for MeaningRepresentation Verifiability Unambiguous Representation Canonical Form Inference ExpressivenessVerifiability System can match input representationagainst representations in knowledgebase. If it finds a match, it can returnYes; Otherwise No. Does Maharani serve vegetarian food?Serves(Maharani,vegetarian food)Unambiguous Representation Single linguistic input can have differentmeaning representations Each representation unambiguouslycharacterizes one meaning. Example: small cars and motorcycles areallowed car(x) & small(x) & motorcycle(y) & small(y) &allowed(x) & allowed(y) car(x) & small(x) & motorcycle(y) & allowed(x) &allowed(y)Ambiguity and Vagueness An expression is ambiguous if, in a givencontext, it can be disambiguated to have aspecific meaning, from a number of discrete,possible meanings. E.g., bank (financialinstitution) vs bank (river bank) An expression is vague, if it refers to a range ofa scalar variable, such that, even in a specificcontext, it’s hard to specify the range entirely.E.g., he’s tall, it’s warm, etc.3Representing Similar Concepts Distinct inputs could have the same meaning Does Maharani have vegetarian dishes? Do they have vegetarian food at Maharani? Are vegetarian dishes served at Maharani? Does Maharani serve vegetarian fare? Alternatives Four different semantic representations Store all possible meaning representations in KBCanonical Form Solution: Inputs that mean same thinghave same meaning representation Is this easy? No! Vegetarian dishes, vegetarian food,vegetarian fare Have, serve What to do?How to Produce aCanonical Form Systematic Meaning Representations can bederived from thesaurus food ___ dish ___|____one overlapping meaning sense fare ___| We can systematically relate syntacticconstructions [S [NP Maharani] serves [NP vegetariandishes]] [S [NP vegetarian dishes] are served at [NPMaharani]]Inference Consider a more complex request Can vegetarians eat at Maharani? Vs: Does Maharani serve vegetarian food? Why do these result in the same answer? Inference: Draw conclusions about truthof propositions not explicitly stored in KB serve(Maharani,VegetarianFood) =>CanEat(Vegetarians,AtMaharani)4Non-Yes/No Questions Example: I'd like to find a restaurantwhere I can get vegetarian food.serve(x,VegetarianFood) Matching succeeds only if variable xcan be replaced by known object inKB.Meaning Structure of Language Human Languages Display a basic predicate-argument structure Make use of variables Make use of quantifiers Display a partially compositional semanticsCompositionality The compositionality principle is animportant principle in formal semantics: The meaning of an expression is a strictfunction of the meanings of its parts It allows to build meaningrepresentations incrementally Standard predicate logic does not adhereto this principle (donkey sentences)Predicate-Argument Structure Represent concepts and relationships among them Some words act like arguments and some words actlike predicates: Nouns as concepts or arguments: red(ball) Adj, Adv, Verbs as predicates: red(ball) Subcategorization (argument) frames specify number,position, and syntactic category of arguments Examples: NP give NP2 NP1 NP give NP1 to NP2 give(x,y,z)5Semantic (thematic) Roles Semantic Roles: Participants in an event Agent: George hit Bill. Bill was hit by George Patient: George hit Bill. Bill was hit by George Semantic (Selectional) Restrictions: Constrain thetypes of arguments verbs take George assassinated the senator *The spider assassinated the fly Verb subcategorization: Allows linking arguments insurface structure with their semantic roles Prepositions are like verbs Under(ItalianRestaurant,$15)First Order Predicate Calculus(FOPC) FOPC provides sound computationalbasis for verifiability, inference,expressiveness Supports determination of truth Supports compositionality of meaning Supports question-answering (via variables) Supports inferenceFOPC Syntax Terms Constants: Maharani Functions: LocationOf(Maharani) Variables: x in LocationOf(x) Predicates: Relations that hold among objects Serves(Maharani,VegetarianFood) Logical Connectives: Permit compositionality ofmeaning I only have $5 and I don’t have a lot of time Have(I,$5) Have(I,LotofTime)! "¬FOPC Semantics Sentences in FOPC can be assignedtruth values True or False6Variables and Quantifiers Existential (∃): There exists A restaurant that serves Mexican food near UMD(∃x) Restaurant(x) Serves(x,MexicalFood)Near(LocationOf(x),LocationOf(UMD)) Universal (∀): For all All vegetarian restaurants serve vegetarian food(∀x) VegetarianRestaurant(x) ->Serves(x,VegetarianFood)! "! "FOPC Examples John gave Mary a book Previously: Give(John,Mary,book) Better:(∃x) Giving(x) Giver(John,x) Givee(Mary,x) Given(book,x) Full Definition of Give:(∃w,x,y,z) Giving(x) Giver(w,x) Givee(z,x) Given(y,x)! "! "! "! "! "! "Why use Variables? Multiple sentences containing “eat” I ate. I ate a turkey sandwich. I ate a turkey sandwich at my desk. I ate at my desk. I ate lunch. I ate a turkey sandwich for lunch I ate a turkey sandwich for lunch at my desk. Seven different