CS 4705 Semantic Analysis: Syntax-Driven Semantics

Semantics and Syntax Some representations of meaning: The cat howls at the moon. –Logic: howl(cat,moon) –Frames: Event: howling Agent: cat Patient: moon How do we decide what we want to represent? –Entities, categories, events, time, aspect –Predicates, arguments (constants, variables) –And…quantifiers, operators (e.g. temporal) Today: How can we compute meaning about these categories from these representations?

Compositional Semantics Assumption: The meaning of the whole is comprised of the meaning of its parts –George cooks. Dan eats. Dan is sick. –Cook(George) Eat(Dan) Sick(Dan) –If George cooks and Dan eats, Dan will get sick. (Cook(George) ^ eat(Dan))  Sick(Dan) Meaning derives from –The people and activities represented (predicates and arguments, or, nouns and verbs) –The way they are ordered and related: syntax of the representation, which may also reflect the syntax of the sentence

Syntax-Driven Semantics S NP VP eat(Dan) Nom V N Dan eats So….can we link syntactic structures to a corresponding semantic representation to produce the ‘meaning’ of a sentence in the course of parsing it?

Specific vs. General-Purpose Rules We don’t want to have to specify for every possible parse tree what semantic representation it maps to We want to identify general mappings from parse trees to semantic representations One approach: –Augment the lexicon and the grammar (as we did with feature structures) –Devise a mapping between rules of the grammar and rules of semantic representation (Rule-to-Rule Hypothesis: such a mapping can be found)

Semantic Attachments Extend each grammar rule with instructions on how to map the components of the rule to a semantic representation S  NP VP {VP.sem(NP.sem)} Each semantic function defined in terms of the semantic representation of choice Problem: how to define these functions and how to specify their composition so we always get the meaning representation we want from our grammar?

A Simple Example McDonald’s serves burgers. Associating constants with constituents –ProperNoun  McDonald’s {McDonald’s} –PlNoun  burgers {burgers} Defining functions to produce these from input –NP  ProperNoun {ProperNoun.sem} –NP  PlNoun {PlNoun.sem} –Assumption: meaning representations of children are passed up to parents for non-branching constuents Verbs are where the action is

–V  serves {E(e,x,y) Isa(e,Serving) ^ Server(e,x) ^ Served(e,y)} where e = event, x = agent, y = patient –Will every verb have its own distinct representation? McDonald’s hires students. McDonald’s gave customers a bonus. Predicate(Agent, Patient, Beneficiary) Once we have the semantics for each consituent, how do we combine them? –VP  V NP {V.sem(NP.sem)} –Goal for VP semantics: E(e,x) Isa(e,Serving) ^ Server(e,x) ^ Served(e,Meat) –VP.sem must tell us Which variables to be replaced by which arguments How this replacement is done

Lambda Notation Extension to First Order Predicate Calculus x P(x) + variable(s) + FOPC expression in those variables Lambda binding Apply lambda-expression to logical terms to bind lambda-expression’s parameters to terms (lambda reduction) Simple process: substitute terms for variables in lambda expression xP(x)(car) P(car)

Lambda Notation Provides Means Formal parameter list makes variables within body of logical expression available for binding to external arguments provided by semantics of other constituents (e.g. NPs) –Lambda reduction implements replacement Semantic attachment for –V  serves {V.sem(NP.sem)} {E(e,x,y) Isa(e,Serving) ^ Server(e,y) ^ Served(e,x)} converts to the lambda expression: { x E(e,y) Isa(e,Serving) ^ Server(e,y) ^ Served(e,x)} –Now ‘x’ is available to be bound when V.sem is applied to NP.sem of direct object (V.sem(NP.sem))

– application binds x to value of NP.sem (burgers) – -reduction replaces x within -expression with burgers –Value of VP.sem becomes: {E(e,y) Isa(e,Serving) ^ Server(e,y) ^ Served(e,burgers)} Similarly, we need a semantic attachment for S  NP VP {VP.sem(NP.sem)} to add the subject NP to our semantic representation of McDonald’s serves burgers –Back to V.sem for serves –We need another -expression in the value of VP.sem –But currently V.sem doesn’t give us one –So, we change it to include another argument to be bound later –V  serves { x y E(e) Isa(e,Serving) ^ Server(e,y) ^ Served(e,x)}

–Value of VP.sem becomes: { y E(e) Isa(e,Serving) ^ Server(e,y) ^ Served(e,burgers)} VP  V NP {V.sem(NP.sem)} binds the outer - expression to the object NP (burgers) but leaves the inner -expression for subsequent binding to the subject NP when the semantics of S is determined S  NP VP {VP.sem(NP.sem)} { y E(e) Isa(e,Serving) ^ Server(e,y) ^ Served(e,burgers)}(McDonald’s) {E(e) Isa(e,Serving) ^ Server(e,McDonald’s) ^ Served(e,burgers)}

But this is just the tip of the iceberg…. For example, terms can be complex A restaurant serves burgers. –‘a restaurant’: E x Isa(x,restaurant) –E e Isa(e,Serving) ^ Server(e, ) ^ Served(e,burgers) –Allows quantified expressions to appear where terms can by providing rules to turn them into well-formed FOPC expressions Issues of quantifier scope Every restaurant serves burgers. Every restaurant serves every burger.

Semantic representations for other constituents? –Adjective phrases: Happy people, cheap food, purple socks intersective semantics Nom  Adj Nom { x Nom.sem(x) ^ Isa(x,Adj.sem)} Adj  cheap {Cheap} x Isa(x, Food) ^ Isa(x,Cheap) …works ok … But….fake gun? Local restaurant? Former friend? Would- be singer? Ex Isa(x, Gun) ^ Isa(x,Fake)

Doing Compositional Semantics To incorporate semantics into grammar we must –Figure out right representation for each constituent based on the parts of that constituent (e.g. Adj) –Figure out the right representation for a category of constituents based on other grammar rules, making use of that constituent (e.g. V.sem) This gives us a set of function-like semantic attachments incorporated into our CFG –E.g. Nom  Adj Nom { x Nom.sem(x) ^ Isa(x,Adj.sem)}

What do we do with them? As we did with feature structures: –Alter, e.g., an Early-style parser so when constituents (dot at the end of the rule) are completed, the attached semantic function applied and meaning representation created and stored with state Or, let parser run to completion and then walk through resulting tree running semantic attachments from bottom-up

Option 1 (Integrated Semantic Analysis) S  NP VP {VP.sem(NP.sem)} –VP.sem has been stored in state representing VP –NP.sem stored with the state for NP –When rule completed, retrieve value of VP.sem and of NP.sem, and apply VP.sem to NP.sem –Store result in S.sem. As fragments of input parsed, semantic fragments created Can be used to block ambiguous representations

Drawback You also perform semantic analysis on orphaned constituents that play no role in final parse Case for pipelined approach: Do semantics after syntactic parse

Non-Compositional Language What do we do with language whose meaning isn’t derived from the meanings of its parts –Non-compositional modifiers: fake, former, local –Metaphor: You’re the cream in my coffee. She’s the cream in George’s coffee. The break-in was just the tip of the iceberg. This was only the tip of Shirley’s iceberg. –Idioms: The old man finally kicked the bucket. The old man finally kicked the proverbial bucket. –Deferred reference: The ham sandwich wants his check. Solutions? Mix lexical items with special grammar rules? Or???

Summing Up Hypothesis: Principle of Compositionality –Semantics of NL sentences and phrases can be composed from the semantics of their subparts Rules can be derived which map syntactic analysis to semantic representation (Rule-to-Rule Hypothesis) –Lambda notation provides a way to extend FOPC to this end –But coming up with rule2rule mappings is hard Idioms, metaphors perplex the process

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