Lecture 12: Semantics IIProfessor Robert C. [email protected]/9.611J SP11The Menu Bar• Administrivia: Projects• What knowledge do we need beyond syntax?• How should we represent this?• How can we learn it?• From last time: representing ‘meaning’ as logicalstatements…we left off here…6.863J/9.611J SP11Quantifier Order• Gilly swallowed a goldfish in a booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), exists(booth, location(e)), …• Gilly swallowed a goldfish in every booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), all(booth, location(e)), …• Does this mean what we’d expect??∃g goldfish(g), swallowee(e,g)∀b booth(b)⇒location(e,b)says that there’s only one eventwith a single goldfish getting swallowedthat took place in a lot of booths ...6.863J/9.611J SP11Quantifier Order• Groucho Marx celebrates quantifier order ambiguity:• In this country a woman gives birth every 15 minutes• Our job is to find that woman and stop her• ∃woman (∀15min gives-birth-during(woman, 15min))• ∀15min (∃woman gives-birth-during(15min, woman))• Surprisingly, both are possible in natural language!• Which is the joke meaning (where it’s always the same woman) andwhy?6.863J/9.611J SP11Quantifier Order• Gilly swallowed a goldfish in a booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), exists(booth, location(e)), …• Gilly swallowed a goldfish in every booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), all(booth, location(e)), …∃g goldfish(g), swallowee(e,g)∀b booth(b)⇒location(e,b)• Does this mean what we’d expect??• It’s ∃e ∀b which means same event for every booth• Probably false unless Gilly can be in every boothduring her swallowing of a single goldfish6.863J/9.611J SP11• Gilly swallowed a goldfish in a booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), exists(booth, location(e)), …• Gilly swallowed a goldfish in every booth• ∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish,swallowee(e)), all(booth, λb location(e,b))Quantifier Order• Other reading (∀b ∃e) involves quantifier raising:• all(booth, λb [∃e past(e), act(e,swallowing), swallower(e,Gilly), exists(goldfish, swallowee(e)), location(e,b)])• “for all booths b, there was such an event in b”6.863J/9.611J SP11Intensional Arguments• Willy wants a unicorn• ∃e act(e,wanting), wanter(e,Willy), exists(unicorn, λu wantee(e,u))• “there is a unicorn u that Willy wants”• here the wantee is an individual entity• ∃e act(e,wanting), wanter(e,Willy), wantee(e, λu unicorn(u))• “Willy wants any entity u that satisfies the unicorn predicate”• here the wantee is a type of entity• Willy wants Lilly to get married• ∃e present(e), act(e,wanting), wanter(e,Willy),wantee(e, λe' [act(e’,marriage), marrier(e',Lilly)])• “Willy wants any event e’ in which Lilly gets married”• Here the wantee is a type of event• Sentence doesn’t claim that such an event exists• Intensional verbs besides want: hope, doubt, believe,…6.863J/9.611J SP11Intensional Arguments• Willy wants a unicorn• ∃e act(e,wanting), wanter(e,Willy), wantee(e, λg unicorn(g))• “Willy wants anything that satisfies the unicorn predicate”• here the wantee is a type of entity• Problem (a fine point I’ll gloss over):• λg unicorn(g) is defined by the actual set of unicorns(“extension”)• But this set is empty: λg unicorn(g) = λg FALSE = λg dodo(g)• Then wants a unicorn = wants a dodo. Oops!• So really the wantee should be criteria for unicornness(“intension”)• Traditional solution involves “possible-world semantics”• Can imagine other worlds where set of unicorns ≠ set of dodos6.863J/9.611J SP11Control• Willy wants Lilly to get married• ∃e present(e), act(e,wanting), wanter(e,Willy),wantee(e, λf [act(f,marriage), marrier(f,Lilly)])• Willy wants to get married• Same as Willy wants Willy to get married• Just as easy to represent as Willy wants Lilly …• The only trick is to construct the representation from thesyntax. The empty subject position of “to get married” is saidto be controlled by the subject of “wants.”6.863J/9.611J SP11Nouns and Their Modifiers• expert• λg expert(g)• big fat expert (cf, big fat Greek wedding…)• λg big(g), fat(g), expert(g)• But: bogus expert• Wrong: λg bogus(g), expert(g)• Right: λg (bogus(expert))(g) … bogus maps to new concept• Boston expert (white-collar expert, TV expert …)• λg Related(Boston, g), expert(g) – expert from Boston• Or with different intonation:• λg (Modified-by(Boston, expert))(g) – expert on Boston• Can’t use Related for that case: law expert and dog catcher= λg Related(law,g), expert(g), Related(dog, g), catcher(g)= dog expert and law catcher6.863J/9.611J SP11Nouns and Their Modifiers• the goldfish that Gilly swallowed• every goldfish that Gilly swallowed• three goldfish that Gilly swallowedOr for real: λg [goldfish(g), ∃e [past(e), act(e,swallowing), swallower(e,Gilly), swallowee(e,g) ]] λg [goldfish(g), swallowed(Gilly, g)] • three swallowed-by-Gilly goldfishlike an adjective!6.863J/9.611J SP11Adverbs• Lili passionately wants Billy• Wrong?: passionately(want(Lili,Billy)) = passionately(true)• Better: (passionately(want))(Lili,Billy)• Best: ∃e present(e), act(e,wanting), wanter(e,Lili),wantee(e, Billy), manner(e, passionate)• Lili often stalks Billy• (often(stalk))(Lili,Billy)• many(day, λd ∃e present(e), act(e,stalking), stalker(e,Lili),stalkee(e, Billy), during(e,d))• Lili obviously likes Billy• (obviously(like))(Lili,Billy) – one reading• obvious(likes(Lili, Billy)) – another reading6.863J/9.611J SP11Speech Acts• What is the meaning of a full sentence?• Depends on the punctuation mark at the end. J• Billy likes Lili. à assert(like(B,L))• Billy likes Lili? à ask(like(B,L))• or more formally, “Does Billy like Lili?”• Billy, like Lili! à command(like(B,L))• Let’s try to do this a little more precisely, using event variablesetc.6.863J/9.611J SP11Speech Acts• What did Gilly swallow?• ask(λx ∃e past(e), act(e,swallowing), swallower(e,Gilly), swallowee(e,x))•
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