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Semantic Analysis Read J & M Chapter 15.

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The Principle of Compositionality There’s an infinite number of possible sentences and an infinite number of possible meanings. But we need to specify the relationship between the two with a finite number of rules. What finite classes can we work with: Words Grammar rules So we need to find a way to define the meaning of an entire sentence as a function of the meaning of the words it contains and the rules that are used to put those words together.

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Deriving the Meaning of Sentences John saw Bill. e Isa(e, Seeing) Agent(e, John) AE(e, Bill) S NPVP PN VNP John saw PN Bill

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Attaching Semantic Rules to Grammar Rules John saw Bill. e Isa(e, Seeing) Agent(e, John) AE(e, Bill) S NPVP PN VNP John saw PN Bill A …{f( .sem, .sem …) PN John{John} { e Isa(o,Person) Name(o, John)} NP PN{PN.sem}

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Handling the Verb S NPVP PN VNP John saw PN Bill S NP VP{VP.sem(NP.sem)} NP PN{PN.sem} PN John{John} PN Bill{Bill} VP V NP{V.sem(NP.sem)} V saw { x y e Isa(e, Seeing) Agent(e,y) AE(e,x) }

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Common NPs John has a cat. S NPVP PN VNP John has DET Nom a N cat e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat)

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When Arguments Are Quantified e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat) S NP VP{VP.sem(NP.sem)} NP PN{PN.sem} NP DET Nom{DET.sem x Nom.sem} PN John{John} DET a{ } Nom N{Isa(x N.sem)} N cat{cat} VP V NP{V.sem(NP.sem)} V has{ x y e Isa(e, Owning) Agent(e,y) AE(e,x) }

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We Get the Wrong Answer The answer we want: e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat) The answer we’re going to get as things stand now: e Isa(e, Owning) Agent(e, John) AE(e, x Isa(x, Cat)) This isn’t even a valid formula.

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Complex Terms A complex term has the following structure: Using one in our example, we get: e Isa(e, Owning) Agent(e, John) AE(e, ) Now we add the following rewrite rule for converting complex terms to ordinary FOPC expressions: P( ) Quantifer variable body Connective P(variable) In this case: AE(e, ) x Isa(x, Cat) AE(e, x) Note: If Quantifier is then Connective is . If , then it’s .

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The Revised Grammar S NP VP{VP.sem(NP.sem)} NP PN{PN.sem} NP DET Nom{ } PN John{John} DET a{ } Nom N{ z Isa(z, N.sem)} N cat{cat} VP V NP{V.sem(NP.sem)} V has{ x y e Isa(e, Owning) Agent(e,y) AE(e,x) }

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Do We Yet Have the Right Answer? The answer we’ve got now: e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat) But suppose we want something like: x Isa (x, Cat) Owner-of(x, John) In this case, we can view our initial answer as an intermediate representation and use it to form whatever other answer we like by applying inference rules.

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Or Suppose We Want a Completely Different Kind of Representation

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More on Quantifiers Everyone ate a cookie. S NP VP{VP.sem(NP.sem)} NP Pro{Pro.sem} NP DET Nom{ } DET a{ } Nom N{ z Isa(z, N.sem)} Pro everyone{ } N cookie{cookie} VP V NP{V.sem(NP.sem)} V ate{ x y e Isa(e, Eating) Agent(e,y) AE(e,x) } e x x' Isa(e, Eating) (person(x') Agent(e, x')) Isa(x, cookie) AE(e,x)

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Different Argument Structures John served Bill. John served steak. S NP VP{VP.sem(NP.sem)} NP PN{PN.sem} NP MassN{MassN.sem} MassN steak{steak} PN John{John} PN Bill{Bill} VP V NP{V.sem(NP.sem)} VP V NP 1 NP 2 {V.sem(NP 1.sem)(NP 2.sem) V served{ x y e Isa(e, Serving) Agent(e,y) AE(e,x) } V served{ x y e Isa(e, Serving) Agent(e,y) Ben(e,x) } V served{ x y z e Isa(e, Serving) Agent(e,z) AE(e,y) Ben(e, x)}

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Sentences that Aren’t Declarative Close the window. S VP{IMP(VP.sem(DummyYou))} Do you sell pretzels? S Aux NP VP{YNQ(VP.sem(NP.sem))} Who sells pretzels? S WhPro VP {WHQ(x, VP.sem(x)}} WHQ(x, e Isa(e, Selling) Agent(e,x) AE(e, pretzels)

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Compound Noun Phrases leather jacket{ x Isa(x, jacket) NN(x, leather)} riding jacket winter jacket letter jacket Nom N { x Isa(x, N.sem)} Nom N Nom { x Nom.sem(x) NN(x, N.sem)} N jacket{jacket} N leather{leather}

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Compound NPs, an Alternative leather jacket{ x Isa(x, jacket) madeof(x, leather)} riding jacket{ x Isa(x, jacket) usedfor(x,riding)} winter jacket letter jacket Nom N { x Isa(x, N.sem)} Nom N Nom { x Nom.sem(x) madeof(x, N.sem)} Nom N Nom { x Nom.sem(x) usedfor(x, N.sem)} N jacket{jacket} N leather{leather} N winter{winter}

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Infinitive Verb Phrases I told Mary to eat. S NPVP ProVNPVPto I toldPN infToVP Mary to V eat e, f Isa(e, telling) Isa(f, eating) Agent(e, Speaker) Ben(e, Mary) AE(e, f) Agent(f, Mary)

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Noncompositional Semantics Coupons are just the tip of the iceberg. That’s just the tip of Mrs. Ford’s iceberg. John kicked the bucket. John would have kicked the bucket. # The bucket was kicked by John. She turned up her toes. # She turned up his toes. Mary threw in the towel. Mary thought about throwing in the towel. # Mary threw in the white towel. willy nilly pell mell helter skelter

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Semantic Grammars If we know we have a limited semantic representation, then build a grammar that is less general and that maps more directly to the semantic interpretation we want.

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Example – Eating Italian Food

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An Alternative InfoRequest I want to go (to) eat (some) FoodType Time {Retrieve (x, isa(x, Restaurant) nationality(x, FoodType.sem))} FoodType Nationality (food){Nationality.sem} Retrieve(x, isa(x, Restaurant) nationality(x, Italian))

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