Semantic Analysis Read J & M Chapter 15.
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.
Deriving the Meaning of Sentences John saw Bill. e Isa(e, Seeing) Agent(e, John) AE(e, Bill) S NP VP PN V NP John saw PN Bill
Attaching Semantic Rules to Grammar Rules John saw Bill. e Isa(e, Seeing) Agent(e, John) AE(e, Bill) S NP VP PN V NP John saw PN Bill A … {f(.sem, .sem …) PN John {John} {e Isa(o,Person) Name(o, John)} NP PN {PN.sem}
Handling the Verb S NP VP PN V NP 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) }
Common NPs John has a cat. e,x Isa(e, Owning) Agent(e, John) AE(e, x) Isa(x, Cat) S NP VP PN V NP John has DET Nom a N cat
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) }
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.
Complex Terms A complex term has the following structure: <Quantifier variable body> Using one in our example, we get: e Isa(e, Owning) Agent(e, John) AE(e, < x Isa(x, Cat)>) Now we add the following rewrite rule for converting complex terms to ordinary FOPC expressions: P(<Quantifier variable body>) Quantifer variable body Connective P(variable) In this case: AE(e, < x Isa(x, Cat)>) x Isa(x, Cat) AE(e, x) Note: If Quantifier is then Connective is . If , then it’s .
The Revised Grammar S NP VP {VP.sem(NP.sem)} NP PN {PN.sem} NP DET Nom {<DET.sem x Nom.sem(x)>} 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) }
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.
Or Suppose We Want a Completely Different Kind of Representation
More on Quantifiers Everyone ate a cookie. S NP VP {VP.sem(NP.sem)} NP Pro {Pro.sem} NP DET Nom {<DET.sem x Nom.sem(x)>} DET a {} Nom N {z Isa(z, N.sem)} Pro everyone {< x person(x)>} 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)
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 NP1 NP2 {V.sem(NP1.sem)(NP2.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)}
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)
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}
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}
Infinitive Verb Phrases I told Mary to eat. S NP VP Pro V NP VPto I told PN infTo VP Mary to V eat e, f Isa(e, telling) Isa(f, eating) Agent(e, Speaker) Ben(e, Mary) AE(e, f) Agent(f, Mary)
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
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.
Example – Eating Italian Food
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))
