1. Introduction to Semantics To be able to reason about the meanings of utterances, we need to have ways of representing the meanings of utterances. A formal structure for representing meaning is called a meaning representation. “the frameworks that are used to specify the syntax and semantics of these representations will be called meaning representation languages.” [p.501]

2. Semantic analysis Just as we performed syntactic analysis on input to build a syntactic representation for that input, we will perform semantic analysis on an input to build a semantic representation for it. We will focus on literal meanings, not metaphorical meanings. Next we introduce desirable properties of a semantic representation.

3. Verifiability “[verifiability] must be possible to use the representation to determine the relationship between the meaning of a sentence and the world as we know it” [p. 504] “[verifiability] is a system’s ability to compare the state of affairs described by a representation to the state of affairs in some world as modeled in a knowledge base” [p. 505]

4. Unambiguous representations While input may be ambiguous – representations should not be. The same applies to syntactic representations: structures should be unambiguous – which is why an ambiguous sentence gives rise to multiple parse trees. Ex: (p. 505) – I wanna eat someplace that’s close to ICSI.

5. Canonical representation (1) Different inputs which carry same meaning should map into the same meaning representation. Ex. (p. 506) – Does Maharani have vegetarian dishes? – Do they have vegetarian food at Maharani? – Are vegetarian dishes served at Maharani? – Does Maharani serve vegetarian fare? Semantic representation should be the same for all these utterances. Issues: – Food, dish and fare are different words, with distinct senses. They also all share a sense, that of something that is eaten. Choosing the correct sense of a word is called word-sense disambiguation.

6. Canonical representation (2) Previous examples worked off of words with shared senses. Different syntactic forms can also express the same semantic content. Ex. – John likes Mary. – It is Mary that John likes. – Mary is liked by John. Semantic representation should be the same for all three utterances.

7. Inference and Variables Representation must support reasoning. “It must be possible for the system to draw conclusions about the truth of propositions that are not explicitly represented in the knowledge base, but are nevertheless logically derivable from the propositions that are present.” [p. 509] Variables used for indefinites (and other things too). Ex: – a restaurant serving vegetarian food – serves(X, vegetarian)

8. Expressiveness Meaning representation must be expressive enough to capture all relevant aspects of meaning expressed in utterances.

9. Meaning Structure of Language Predicate-argument structure – captures relationships holding between entities in sentence – not only verbs act as predicates (prepositions, adjectives, …) – syntactic roles of constituents are expressed by subcategorization (e.g. direct object) – semantic roles of arguments are expressed by thematic (or case) roles (e.g. theme)

10. A meaning representation language First-order predicate calculus (FOPC) can be used as a meaning representation language. Must give syntax and semantics of the FOPC.

11. Syntax of FOPC (p. 514) Formula  AtomicFormula | Formula Connective Formula | Quantifier Variable, … Formula | ~Formula | ( Formula ) AtomicFormula  Predicate(Term,…) Term  Function(Term,…) | Constant | Variable Connective   |  |  Quantifer   |  Constant  VegetarianFood | Maharani | … Variable  x | y | … Predicate  Serves | Near | … Function  LocationOf | CuisineOf | …

12. Semantics of FOPC Semantics tie representation to domain/real world Terms map onto individuals in the domain Formulae map onto {true, false} – f  g is true iff both f and g are true, false otherwise – f  g is false iff both f and g are false, true otherwise – f  g is false iff f is true and g is false, true otherwise –  x f(x) is true iff f(x) is true for each substitution of an individual from the domain in place of x, false otherwise –  x f(x) is false iff f(x) is false for each substitution of an individual from the domain in place of x, true otherwise

13. Inference modus ponens – Reasoning from antecedent to consequence in if- then statements – E.g. Suppose you know that If John is hungry then John eats pizza. (X  Y) John is hungry. (X) You can then conclude from the above, using modus ponens, that Y holds.

14. Forward chaining Using modus ponens to reason from antecedent to consequent. It is used to find all the consequences of a rule base: a  ba  c b  de  f d  f  g a Forward chaining finds b, c, d. f and g are not derivable. + finds everything derivable from a knowledge base – finds everything derivable from a knowledge base

15. Backward chaining Using modus ponens to prove a consequent by proving an antecedent. Consider the same rule base: a  ba  c b  de  f d  f  g a Backward chaining on d succeeds: – d is proved if b can be proved; b can be proved if a can be proved; a can be proved because a is known. Backward chaining on g fails: – g is proved if d  f is proved; d  f is proved if d is proved and f is proved; d is proved (see above); f is proved if e is proved. e cannot be proved. FAIL!

16. Categories relation vs. object tension One way to express that Katsura is a Japanese restaurant is to introduce a one- place relation JapaneseRestaurant and make it hold of the individual Katsura: – JapaneseResaurant(Katsura) The problem is that I can’t reason about the category JapaneseRestaurant, as in: – myFavorite(JapaneseRestaurant,Katsura) – myFavorite(IndianRestaurant,Pushap)

17. Reification Reification means objectification Make JapaneseRestaurant an object – JapaneseResaurant(Katsura) is expressed as: (this is a member-class relationship) – ISA(Katsura, JapaneseResaurant) We can express subclass relationships using AKO (A Kind Of): – AKO(JapaneseRestaurant, Restaurant)

18. Events Can represent events as relations: – Make a reservation for this evening for a table for two persons at 8. – Reservation(Hearer, Maharani, Today, 8PM, 2) Can’t reason about the event! Reify the event: – ISA(e,Reservation) ^ Agent(e,Hearer) ^ Restaurant(e,Maharani) ^ Day(e,Today) ^ Time(e,8PM) ^ PartySize(e,2)