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Semantics (Representing Meaning)

Semantics (Representing Meaning). Allen ’ s Chapter 8 J&M ’ s Chapter 14. Logical Forms. Logical form of a sentence is the context-independent meaning of the sentence “Meaning” has different usages: A warm engine means that the car has been used (implication)

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Semantics (Representing Meaning)

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  1. Semantics (Representing Meaning) Allen’s Chapter 8 J&M’s Chapter 14

  2. Logical Forms • Logical form of a sentence is the context-independent meaning of the sentence • “Meaning” has different usages: • A warm engine means that the car has been used (implication) • “Amble” means to walk slowly (definition) • We need a formal language in which we can specify meaning without having to refer back to natural language itself

  3. Semantic Interpretation versus Contextual Interpretation • Do you know what gate you are going to? • Yes. • Which gate is it? • Therefore, question 1 means different things in different contexts • Can we define a notion of sentence meaning that is independent of context? The primary advantage is modularity: • study sentence meaning in detail without all the complications of sentence usage • Meaning: context independent sense, versus • Usage: context dependent aspects

  4. Semantic Interpretation • The representation of context-independent meaning is called the logical form • The process of mapping a sentence to its logical form is called semantic interpretation • The process of mapping the logical form to the final knowledge representation language is called contextual interpretation

  5. Semantic Interpretation John drove to the store. WM1 WM2 WM3 WM4 WM5 (logical form) Context World knowledge (interpretation, conclusions)

  6. Semantic Interpretation

  7. Logical Form Languages • In some approaches the logical form is the same as the final knowledge representation language • In that case, the language must be rich enough to represent terms such indexical terms (i.e., terms defined by the context), I, you, the red ball are indexical • Many other aspects of language (e.g., tense, scope of quantifiers) also depend on the context and cannot be uniquely identified at the logical form level

  8. Semantic Ambiguity • Ambiguity is again a serious obstacle during semantic interpretation • A word is semantically ambiguous if it maps to more than one sense • “Kid” is ambiguous between a baby goat and a human child • “horse” is not ambiguous, though there are colts and mares

  9. Test for semantic Ambiguity • Certain syntactic constructs require identical class of objects • I have two kids and George has three • I have one horse and George has two • All senses involve some degree of vagueness • I ran last year and George did too

  10. Level of ambiguities • The ambiguity might come from syntactic ambiguity Happy cats and dogs live on the farm • Some may come from the scope of quantifiers Every boy loves a dog  d. Dog(d) &  b. Boy(b)  Loves(b, d)  b. Boy(b) &  d. Dog(d)  Loves(b, d) • Quantifiers vary with respect to vagueness Many people saw the accident • Indexical terms are not considered semantically ambiguous The dog, I, here, …

  11. Using Constraints to remove ambiguities • Some context-independent constraints can disambiguate indexical terms Jack saw him in the mirror, Jack saw himself in the mirror • A very important aspect of context-independent meaning is Co-occurrence constraints between word senses Jack ran the printing press for years (transitive) Jack ran in the park (intransitive) Jack ran in the election (intransitive) • One of the most important tasks of semantic interpretation is to utilize these constraints to reduce the number of possible senses of each word

  12. The basic logical form language • The primitive unit of meaning is the word sense • These primitives are combined to form the meaning of more complex expressions, using a language similar to FOPC • Word senses serve as atoms or constants • Abstract objects such as events and situations are represented by terms • Relations and properties are represented by predicates

  13. Examples: • Fido is a dog is represented as (DOG1 FIDO1) • Sue does not love Jack (NOT (LOVE1 SUE1 JACK1)) • I went home and had a drink • A man entered the room. He walked over the table. ( x P(x) &  x Q(x)) • Need for generalized quantifiers: All, some, more, many, a few, the, a , etc.

  14. Common Qusntifiers

  15. Generalized quantifiers All dogs bark and most people laughed (quantifier variable : restriction proposition body proposition) The logical form of • Most dogs bark : (MOST d1 : (DOG1 d1) (BARK1 d1)) • Most barking things are doges: (MOST d2 : (BARK1 d2) (DOG1 d2))

  16. Generalized quantifiers (Cont.) • The dog barks: (THE x : (DOG1 x) (BARKS1 x)) • The happy dog barks: (THE x : (& (DOG1 x) (HAPPY x)) (BARKS1 x)) • The dogs bark: (THE x : ((PLUR DOG1) x) (BARKS1 x)) Distributive reading • The dogs met at the corner Collective reading • Two men bought a stereo is ambiguous

  17. Semantic Networks Vs FOPC

  18. Modal Operators • Modal operators are needed to represent the meaning of verbs such as believe and want, and for tense, and other modalities • Modal operators look similar to logical operators, but have major differences: • Terms within the scope of a modal operator may have an interpretation that differs from the logical one • Let’s assume Jack is known as John to some people, If (JACK1 = JOHN22) Then (HAPPY1 JACK1) = (HAPPY1 JOHN22), But (BELIEVE1 SUE1 (HAPPY1 JACK1)) is not the same as (BELIEVE1 SUE1 (HAPPY1 JOHN22)) • This is called failure of substitutivity in modal contexts

  19. Modal Operators (Cont.) • Another important class of modal operators for natural language are the tense operators: PAST, PRES, AND FUT (PRES (SEES1 JOHN1 FIDO1)) (PAST (SEES1 JOHN1 FIDO1)) (FUT (SEES1 JOHN1 FIDO1)) • Assume JOHN1 = PRESIDENT1 at now, but not in the past, so it cannot be concluded that (PAST (SEES1 PRESIDENT1 FIDO1)) • A proposition and its negation can be both true in the past (but at different times) (PAST (HAPPY1 JOHN1)) and (PAST (NOT (HAPPY1 JOHN1))) can be both true

  20. Encoding ambiguity in the logical form • A sentence may have multiple possible syntactical structures • Each structure may have multiple logical forms • Each word in the sentence may have multiple senses • Simply generating all possible logical forms is not practical • Instead, certain ambiguities can be represented within the logical form, and later resolved by the context. This is referred to as quasi logical form

  21. Encoding ambiguity in the logical form • Main source of ambiguities in logical forms come from words multiple senses • Some of word senses have different structural properties and can be resolved by the context of the surrounding sentence • But often a word’s different senses have identical structural constraints • A separate logical form is built for each possible combination of senses for the words in the sentence

  22. Encoding ambiguity in the logical form • Anywhere an atomic sense is allowed, a set of possible atomic senses can be used • The noun ball has at least two senses: BALL1, the object used in games, and BALL2, the social event • Sue watched the ball is ambiguous out of context (THE b1 : ({BALL1, BALL2} b1) (PAST (WATCH1 SUE1 b1))) , which abbreviates: • (THE b1 : (BALL1 b1) (PAST (WATCH1 SUE1 b1))) • (THE b1 : (BALL2 b1) (PAST (WATCH1 SUE1 b1)))

  23. Ambiguity regarding scope of quantifiers • Every boy loves a dog (LOVES1 <EVERY b1 (BOY1 b1)> <A d1 (DOG1 d1>) which abbreviates an ambiguity between: • (EVERY b1 : (BOY1 b1) (A d1: (DOG1 d1) (LOVES1 b1 d1))) • (A d1 : (DOG1 d1)(EVERY b1 : (BOY1 b1) (LOVES1 b1 d1))) • A sentence with 4 quantifier would have 4! (24) possible ordering, and with 5 quantifier would have 5! (120) possible ordering

  24. Ambiguity regarding scope of quantifiers • A further abbreviation is used for restriction with unary predicates to drop the variable <EVERY b1 (BOY1 b1)> is abbreviated as: • <EVERY b1 BOY1> • A large number of constructs in natural languages are sensitive to scoping • All generalized quantifier, including THE, are subject to scoping At every hotel, the receptionist was friendly

  25. Ambiguity regarding scope of quantifiers • Operators such as negation and tense are also scope sensitive • Every boy didn’t run is ambiguous between • (NOT (EVERY b1 : (BOY1 b1) (RUN1 b1))) • (EVERY b1 : (BOY1 b1) (NOT (RUN1 b1))) • Quasi logical form of the sentence is: (<NOT RUN1> <EVERY b1 BOY1>)

  26. Proper names and Pronouns • Proper names must be interpreted in context: name John refers to different people in different situations • (NAME <variable> <name>), means that variable has the specified name • John ran is represented as (<PAST RUN1> (NAME j1 “John”)) • Pronouns are indexical and need a special function, too. • (PRO <variable> <proposition>) • Every man liked him (<PAST LIKE1> <EVERY m1 MAN1> (PRO m2 (HE1 m2))), where HE1 is the sense for he and him • “He” is often written as (PRO m2 HE1)

  27. Verbs and states in logical form • John broke the window with the hammer • The hammer broke the window • The window broke • The verb “break” has verb senses of different arity • (<PAST BREAK1> (NAME j1 “John”) <THE w1 WINDOW1> <THE h1 HAMMER1>) • (<PAST BREAK2> <THE h1 HAMMER1> <THE w1 WINDOW1> ) • (<PAST BREAK3> <THE w1 WINDOW1>)

  28. Events in logical form • Introducing events into logical forms: • John broke it ( e1 : BREAK1 e1 (NAME j1 “John”) (PRO i1 IT1)) • John broke it with the hammer ( e1 : (& ( BREAK1 e1 (NAME j1 “John”) (PRO i1 IT1)) (INSTR e1 <THE h1 HAMMER1>))) • Additional modifiers such as, on Tuesday or, in the hallway, etc. can now be added to the basic representation • Only one sense of verb break is needed

  29. Case Grammars • How are noun phrases related to verbs? • Case Grammar claims: number of possible semantic relationships is small • Sentences with different syntax but same meanings: identical case analyses • John broke the window with a hammer. • The hammer broke the window. • The window broke.

  30. Case and Thematic roles • There is only a limited set of abstract semantic relationships that can hold between a verb and its arguments • These are often called thematic or case roles John broke the window is represented as ( e1 : (& ( BREAK1 e1) (AGENT e1 (NAME j1 “John”)) (THEME e1 <THE w1 WINDOW1>))) • General form: ( e : (& (Event-p e) (Relation1e Obj1) … (Relationne Objn))) • Abbreviated as: (Event-p e [Relation1 Obj1] … [Relationn Objn])

  31. Case and Thematic roles • The quasi-logical form of John broke the window is: (<PAST BREAK1> e1 [AGENT (NAME j1 “John”)] [THEME <THE w1 WINDOW1>]) • Verbs other than event verbs can be also represented: Mary is unhappy (<PAST UNHAPPY1> (NAME m1 “Mary”))

  32. Case and thematic roles • Notion of events can be generalized to include states • UNHAPPY is a predicate that asserts its argument is in a state of unhappiness ( s1 <PAST UNHAPPY1> s1 (THEME s1 (NAME m1 “Mary”)) Mary was unhappy in the meeting (<PAST UNHAPPY1> s1 [THEME (NAME m1 “Mary”)] [IN-LOC <THE t1 MEETING1>])

  33. Different forms of representation • With thematic roles, Mary sees John is shown as: (PRES ( l1 (& (SEES1 l1) (AGENT l1 (NAME m1 “Mary”) (THEME l1 (NAME J1 “John”))))) • Abbreviated form of thematic roles: (PRES (SEES1 l1 [AGENT (NAME m1 “Mary”)] [THEME (NAME J1 “John”)])) • Without thematic roles: (PRES (SEES1 (NAME m1 “Mary”) (NAME J1 “John”)))

  34. Determining Thematic Roles • AGENT: instigator of the action (intention, volition, responsibility) • Test: add a phrase like intentionally • John intentionally broke the window. • * The hammer intentionally broke the window • Not all animate subjects are AGENTS • * John intentionally died. • * Mary remembered her birthday in order to get some presents.

  35. Determining Thematic Roles • THEME: entity undergoing a change or being acted upon • usually the syntactic object • for a transitive verb X, THEME is usually the answer to “what was Xed?” • for an intransitive verb, THEME is used for subjects that are not AGENTs • The clouds appeared over the horizon. • John broke the rock. • I gave John the book.

  36. The Structure of Verbs • Can we classify verbs by the semantic roles they require? • Distinguish inner roles (obligatory) from outer roles (optional) • to put (PP / TO-LOC)

  37. The Structure of Verbs (2) • Inner roles can have only one NP: • I ran to the store and to the bank • * I ran to the store to the bank • Outer roles can have multiple NPs: • I saw the play in Rochester at the Eastman • THEME is typically obligatory; AGENT is optional for verbs that can be passivized

  38. Speech Acts • Different sentences have different purposes • Each type of sentence indicates a different relation between the speaker and the receiver • Each types has an operator that takes the sentence interpretation and produces what is called a surface speech act • (ASSERT (Proposition)) • (Y/N-QUERY (Proposition)) • (WH-QUERY (Proposition)) • (COMMAND (Proposition))

  39. Speech Acts (cont.) The man ate a peach (ASSERT (<PAST EAT> e1 [AGENT <THE m1 MAN1>] [THEME <A p1 PEACH>])) Did the man eat a peach? (Y/N-QUERY (<PAST EAT> e1 [AGENT <THE m1 MAN1>] [THEME <A p1 PEACH>])) Eat the peach (COMMAND (EAT e1 [THEME <THE p1 PEACH>]))

  40. Wh questions • A new quantifier WH is needed to represent wh-terms • What : <WH p1 ANYTHING> • Which man : <WH m1 MAN1> • Who : <WH p1 PERSON1> • For how many and how much two more quantifiers HOW-MANY and HOW-MUCH are needed: What did the man eat? (WH-QUERY (<PAST EAT1> e1 [AGENT <THE m1 MAN1>][THEME <WH w1 PHYSOBJ1>]))

  41. Embedded sentences • Embedded sentences do not need any new notation The man who ate a peach left (ASSERT (<PAST LEAVE> e1[AGENT <THE m1 (& (MAN1 m1) (<PAST EAT1> e2 [AGENT m1] [THEME <A p1 PEACH1>))>])

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