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Semantics

Semantics. cCS 224n / Lx 237 Tuesday, May 11 2004. With slides borrowed from Jason Eisner. Objects . Three Kinds: Boolean – semantic value of sentences Entities Objects, NPs Maybe space / time specifications Functions Predicates – function returning a boolean

dorothy-williamson
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Semantics

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  1. Semantics cCS 224n / Lx 237 Tuesday, May 11 2004 With slides borrowed from Jason Eisner

  2. 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.

  3. 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

  4. 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

  5. loves(x,y) died(x) S S x x VP VP NP NP y NP the bucket NP V kicked V loves 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

  6. 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 & 1 argument • To get its semantics, apply function to argument!

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

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

  9. Sfin NP what function should apply to G to yield the desired blue result? (this is like division!) START Punc . VPfin N nation T -s VPstem Det Every loves(G,L) Vstem want Sinf G NP George VPinf VPstem T to NP Laura Vstem love

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

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

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

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

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

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

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

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

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

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

  20. 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

  21. 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.

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