postech semantics

*Semantics: 

*Semantics CS 224n / Lx 237 Tuesday, May 11 2004 With slides borrowed from Jason Eisner

Objects : 

Objects Three Kinds: Boolean – semantic value of sentences Entities Objects, NPs Maybe space / time specifications Functions Predicates – function returning a boolean Functions might return other functions Functions might take other functions as arguments.

Nouns and their modifiers: 

Nouns and their modifiers expert g expert(g) big fat expert g big(g)  fat(g)  expert(g) But: bogus expert Wrong: g bogus(g)  expert(g) Right: g (bogus(expert))(g) … bogus maps to new concept Baltimore expert (white-collar expert, TV expert …) g Related(Baltimore, g)  expert(g) Or with different intonation: g (Modified-by(Baltimore, expert))(g) Can’t use Related for that case: law expert and dog catcher = g Related(law,g)  expert(g)  Related(dog, g)  catcher(g) = dog expert and law catcher

Modifiers continued : 

Modifiers continued Non-intersective adjectives overpriced(in(paloalto)(house)) in(paloalto)(overprice(house)) Adjectives denotation depend precisely on what they are modifying.

Compositional Semantics: 

We’ve discussed what semantic representations should look like. But how do we get them from sentences??? First - parse to get a syntax tree. Second - look up the semantics for each word. Third - build the semantics for each constituent Work from the bottom up The syntax tree is a 'recipe' for how to do it Compositional Semantics

Compositional Semantics: 

Add a 'sem' feature to each context-free rule S  NP loves NP S[sem=loves(x,y)]  NP[sem=x] loves NP[sem=y] Meaning of S depends on meaning of NPs Compositional Semantics

Compositional Semantics: 

Instead of S  NP loves NP S[sem=loves(x,y)]  NP[sem=x] loves NP[sem=y] might want general rules like S  NP VP: V[sem=loves]  loves VP[sem=v(obj)]  V[sem=v] NP[sem=obj] S[sem=vp(subj)]  NP[sem=subj] VP[sem=vp] Now George loves Laura has sem=loves(Laura)(George) In this manner we’ll sketch a version where Still compute semantics bottom-up Grammar is in Chomsky Normal Form So each node has 2 children: 1 function andamp; 1 argument To get its semantics, apply function to argument! Compositional Semantics

Slide8: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc .

Slide9: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) the meaning that we want here: how can we arrange to get it?

Slide10: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) G

Slide11: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) x loves(x,L) G

Slide12: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) We’ll say that 'to' is just a bit of syntax that changes a VPstem to a VPinf with the same meaning.

Slide13: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L)

Slide14: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) x loves(x,L) G a a y x loves(x,y) L x loves(x,L) x wants(x, loves(G,L))

Slide15: 

NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . loves(G,L) x loves(x,L) G a a yx loves(x,y) L x loves(x,L) x wants(x, loves(G,L))

Slide16: 

NP Laura Vstem love VPstem VPinf T to Sinf VPstem Vstem want VPfin T -s N nation Det Every START Punc . x wants(x, loves(G,L)) NP George

Slide17: 

NP Laura Vstem love VPstem VPinf T to Sinf VPstem Vstem want VPfin T -s N nation Det Every START Punc . x present(wants(x, loves(G,L))) NP George

Slide18: 

NP Laura Vstem love VPstem VPinf T to Sinf VPstem Vstem want VPfin T -s N nation Det Every START Punc . present(x wants(x, loves(G,L))) NP George nation

Slide19: 

NP Laura Vstem love VPstem VPinf T to Sinf VPstem Vstem want VPfin T -s N nation Det Every START Punc . NP George s assert(s)

In Summary: From the Words: 

In Summary: From the Words NP Laura Vstem love VPstem VPinf T to Sinf NP George VPstem Vstem want VPfin T -s N nation Det Every START Punc . G a a y x loves(x,y) L y x wants(x,y) v x present(v(x)) every nation s assert(s) assert(present(wants(every(nation), loves(G,L))))

So now what?: 

So now what? Now that we have the semantic meaning, what do we do with it? Huge literature on logical reasoning, and knowledge learning. Reasoning versus Inference 'John ate a Pizza' Q:What was eaten by John? A: pizza 'John ordered a pizza, but it came with anchovies. John then yelled at the waiter and stormed out.' Q: What was eaten by John? A: nothing

Problem 1a: 

Problem 1a Write grammar rules complete with semantic translations that could be added to the grammar fragment, which will parse the above sentence and generate a semantic representation using the own predicate.