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. 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

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

6. 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! Compositional Semantics

7. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc.

8. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. loves(G,L) the meaning that we want here: how can we arrange to get it?

9. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. loves(G,L) G what function should apply to G to yield the desired blue result? (this is like division!)

10. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. loves(G,L) x loves(x,L) G

11. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. loves(G,L) x loves(x,L) G a a x loves(x,L) We’ll say that “to” is just a bit of syntax that changes a VP stem to a VP inf with the same meaning.

12. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. loves(G,L) x loves(x,L) G a a x loves(x,L) y x loves(x,y) L

13. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP 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) ) by analogy

14. NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP 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)) y x wants(x,y) by analogy

15. NP Laura V stem love VP stem VP inf T to S inf VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. x wants(x, loves(G,L)) x present( wants(x, loves(G,L)) ) NP George v x present(v(x))

16. NP Laura V stem love VP stem VP inf T to S inf VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. x present(wants(x, loves(G,L))) NP George present(wants(every(nation), loves(G,L)))) every(nation)

17. NP Laura V stem love VP stem VP inf T to S inf VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. present( x wants(x, loves(G,L))) NP George present(wants(every(nation), loves(G,L)))) every(nation) n every(n) nation

18. NP Laura V stem love VP stem VP inf T to S inf VP stem V stem want VP fin T -s S fin NP N nation Det Every START Punc. NP George present(wants(every(nation), loves(G,L)))) s assert(s)

19. In Summary: From the Words NP Laura V stem love VP stem VP inf T to S inf NP George VP stem V stem want VP fin T -s S fin NP 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)) everynation s assert(s) assert(present(wants(every(nation), loves(G,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.