Semantics: Representations and Analyses

What kinds of meaning do we want to capture? Categories/entities IBM, Jane, a black cat, Pres. Bush Events running a mile, AS elected governor of CA Time Oct 30, next week, in 2 years Aspect Jack knows how to run. Jack is running. Jack ran the mile in 5 min. Beliefs, Desires and Intentions (BDI)

What Can Serve as a Meaning Representation? Anything that allows us to Answer questions (What is the tallest building in the world?) Determine truth (Is the blue block on the red block?) Draw inferences (If the blue block is on the red block and the red block is on the tallest building in the world, then the blue block is on the tallest building in the world)

Meaning Representations All represent ‘linguistic meaning’ of I have a car and state of affairs in some world All consist of structures, composed of symbols representing objects and relations among them FOPC: Semantic Net: having haver had-thing speaker car

Conceptual Dependency Diagram: Car  Poss-By Speaker Frame Having Haver: S HadThing: Car

A Standard Representation: Predicate-Argument Structure Represents concepts and relationships among them Nouns as concepts or arguments (red(ball)) Adjectives, adverbs, verbs as predicates (red(ball)) Subcategorization (or, argument) frames specify number, position, and syntactic category of arguments NP likes NP NP likes Inf-VP NP likes NP Inf-VP

Semantic (Thematic) Roles Subcat frames link arguments in surface structure with their semantic roles Agent: George hit Bill. Bill was hit by George. Patient: George hit Bill. Bill was hit by George. Selectional Restrictions: constraints on the types of arguments verbs take George assassinated the senator. *The spider assassinated the fly. assassinate: intentional (political?) killing

First Order Predicate Calculus Not ideal as a meaning representation and doesn't do everything we want -- but better than many… Supports the determination of truth Supports compositionality of meaning Supports question-answering (via variables) Supports inference

NL Mapping to FOPC Terms: constants, functions, variables Constants: objects in the world, e.g. Huey Functions: concepts, e.g. sisterof(Huey) Variables: x, e.g. sisterof(x) Predicates: symbols that refer to relations that hold among objects in some domain or properties that hold of some object in a domain likes(Huey, kibble) cat(Huey)

Logical connectives permit compositionality of meaning kibble(x)  likes(Huey,x) “Huey likes kibble” cat(Vera) ^ odd(Vera) “Vera is an odd cat” sleeping(Huey) v eating(Huey) “Huey either is sleeping or eating” Sentences in FOPC can be assigned truth values Atomic formulae are T or F based on their presence or absence in a DB (Closed World Assumption?) Composed meanings are inferred from DB and meaning of logical connectives

Limitations: cat(Huey) sibling(Huey,Vera) cat(Huey) ^ sibling(Huey,Vera)  cat(Vera) Limitations: Do ‘and’ and ‘or’ in natural language really mean ‘^’ and ‘v’? Mary got married and had a baby. And then… Your money or your life! Does ‘’ mean ‘if’? If you go, I’ll meet you there. How do we represent other connectives? She was happy but ignorant.

Quantifiers: Existential quantification: There is a unicorn in my garden. Some unicorn is in my garden. Universal quantification: The unicorn is a mythical beast. Unicorns are mythical beasts. Many? A few? Several? A couple?

Temporal Representations How do we represent time and temporal relationships between events? Last year Martha Stewart was happy but soon she will be in prison. Where do we get temporal information? Verb tense Temporal expressions Sequence of presentation Linear representations: Reichenbach ‘47

Utterance time (U): when the utterance occurs Reference time (R): the temporal point-of-view of the utterance Event time (E): when events described in the utterance occur George is eating a sandwich. -- E,R,U  George had eaten a sandwich (when he realized…) E – R – U  George will eat a sandwich. --U,R – E  While George was eating a sandwich his mother arrived.

Verbs and Event Types: Aspect Statives: states or properties of objects at a particular point in time I am hungry. Activities: events with no clear endpoint I am eating. Accomplishments: events with durations and endpoints that result in some change of state I ate dinner. Achievements: events that change state but have no particular duration – they occur in an instant I got the bill.

Beliefs, Desires and Intentions Very hard to represent internal speaker states like believing, knowing, wanting, assuming, imagining Not well modeled by a simple DB lookup approach so.. Truth in the world vs. truth in some possible world George imagined that he could dance. George believed that he could dance. Augment FOPC with special modal operators that take logical formulae as arguments, e.g. believe, know

Mutual belief: I believe you believe I believe…. Believes(George, dance(George)) Knows(Bill,Believes(George,dance(George))) Mutual belief: I believe you believe I believe…. Practical importance: modeling belief in dialogue Clark’s grounding

Compositional Semantics The meaning of the whole is made up of the meaning of its parts (predicates and arguments) 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) Sick(Dan)  Cook(George) Syntax tells us how to combine the parts

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

Rule-to-Rule Hypothesis 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: Hypothesis: A mapping exists between rules of the grammar and rules of semantic representation

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 is 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 AyCaramba serves meat. Associating constants with arguments ProperNoun  AyCaramba {AyCaramba} MassNoun  meat {Meat} Defining functions to produce these from input NP  ProperNoun {ProperNoun.sem} NP  MassNoun {MassNoun.sem} Assumption: meaning reps of children are passed up to parents for non-branching constuents Verbs here are where the action is

How do we combine these pieces? V  serves {E(e,x,y) Isa(e,Serving) ^ Server(e,x) ^ Served(e,y)} Will every verb need its own distinct representation? George served in the army How do we combine these pieces? VP  V NP Goal: E(e,x) Isa(e,Serving) ^ Server(e,x) ^ Served(e,Meat) VP semantics must tell us Which vars to be replaced by which args? How this replacement is done?

Non-Compositional Language What do we do with language whose meaning isn’t derived from the meanings of its parts 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.

Problems with Syntactic-Driven Semantics Syntactic structures often don’t fit semantic structures very well Important semantic elements often distributed very differently in trees for sentences that mean ‘the same’ I like soup. Soup is what I like. Parse trees contain many structural elements not clearly important to making semantic distinctions Syntax driven semantic representations are sometimes pretty bizarre

Sum Many hard problems in full semantic representation: Temporal relations: tense, aspect BDI Current representations impoverished in many respects Next time: Read Ch 16