Semantic Analysis

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))

Semantic Analysis