Semantic Analysis: Syntax-Driven Semantics

1. Semantic Analysis: Syntax-Driven Semantics CS 4705

2. 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?

3. 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

4. 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?

5. 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 amapping between rules of the grammar and rules of semantic representation (Rule-to-Rule Hypothesis: such a mapping can be found)

6. 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?

7. 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

8. 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

9. 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)

10. 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))

11.  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 forserves • 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)}

12. 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)}

13. 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,<E x Isa(x,restaurant)>) ^ 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.

14. 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)

15. 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)}

16. 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

17. 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

18. 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

19. 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???

20. 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

21. Next • Read Ch. 16 • Homework 2 assigned – START NOW!!