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CAS LX 502

CAS LX 502. 11a. Predicate modification and adjectives. Is hungry. As a starting point, we’ve been considering is hungry to be an intransitive verb. Really, though, is is the verb, hungry is an adjective.

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CAS LX 502

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  1. CAS LX 502 11a. Predicate modificationand adjectives

  2. Is hungry • As a starting point, we’ve been considering is hungryto be an intransitive verb. • Really, though, is is the verb, hungry is an adjective. • An individual can either be hungry or not hungry. That is, hungry is either true or false of an individual. Hungry is a function from individuals to truth values, <e,t>. • In is hungry, the verb is is not contributing any meaning, it’s just there to link up the subject and the adjective.

  3. Bond is hungry • Let’s tweak our syntax so that is hungry is comprised of is and hungry, and let’s say that ishas no semantic value, that it is meaningless. • VP  Vbe Adj • Vbe is • Adj  hungry, happy, tall • [Vbe]M,g = — • [hungry]M,g = x [ x  F(hungry) ]

  4. Bond is hungry • To interpret this we want is to be ignored. To be precise, we can slightly modify Pass-Up so that it applies to this case. • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g S NP VP NP Vbe Adj Bond is hungry

  5. Bond is hungry • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g S NP VP NP Vbe Adj Bond is hungry x [ x  F(hungry) ]<e,t>

  6. x [ x  F(hungry) ]<e,t> Bond is hungry • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g S NP VP NP Vbe Adj Bond is hungry x [ x  F(hungry) ]<e,t>

  7. x [ x  F(hungry) ]<e,t> Bond is hungry • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g S NP VP NP Vbe Adj Bond is hungry x [ x  F(hungry) ]<e,t> x [ x  F(hungry) ]<e,t>

  8. x [ x  F(hungry) ]<e,t> Bond is hungry • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g S NP VP NP Vbe Adj Bond is hungry F(Bond) ]<e>

  9. x [ x  F(hungry) ]<e,t> Bond is hungry F(Bond) ]<e> • Pass-UpIf a node b has only one daughter with a semantic value, a, then [b]M,g = [a]M,g • Functional application[ga b ]M,g =[b]M,g ( [a]M,g )or[a]M,g ( [b]M,g ) whichever is defined S NP VP NP Vbe Adj Bond is hungry

  10. x [ x  F(hungry) ]<e,t> Bond is hungry F(Bond) ]<e> • Functional application[ga b ]M,g =[b]M,g ( [a]M,g )or[a]M,g ( [b]M,g ) whichever is defined • [S]M,g = [VP]M,g ( [NP]M,g )= x [ x  F(hungry) ] ( [NP]M,g)= x [ x F(hungry) ] ( F(Bond) )= F(Bond) F(hungry) S NP VP NP Vbe Adj Bond is hungry

  11. Every hungry fish is happy • By separating is from hungry, we’ve isolated a category of adjectives, which also appear in noun phrases modifying a common noun, as in every hungry fish. • Now that we have adjectives, we can turn a common noun like fish into a more descriptive common noun like hungry fish… inching closer to actual English. • NC Adj NC

  12. Nemo is a fish • One more detour before we continue: What is the contribution of a in Nemo is a fish? • We have a listed as a quantifier, meaning essentially the same as some, e.g., • A fish likes every book. • Some fish likes every book. • A a b means that there is an x that for which both a and b hold. • Every a b means that for every x, being a implies also being b.

  13. Nemo is a fish • But does Nemo is a fishreally mean ‘There is an x that is a fish, and Nemo is that x’? • It doesn’t really feel like that. Also, notice that every cannot be used here: • *Nemo is every happy fish.

  14. Nemo is a fish • What it seems like intuitively is that a is not adding anything to the meaning either. That, like is, a is just meaningless, passing along the meaning of the common noun. • So, let’s allow for that by building in a “dummy determiner” that has no meaning and shows up only when the verb is is. • VP  Vbe NPpred • NPpred Detdummy NC • Detdummy  a • [DETdummy a ]M,g = —

  15. Nemo is a fish • There’s nothing new or fancy going on here, just more use of Pass-Up. • [fish]M,g = x [ x  F(fish) ] • [DETdummya]M,g = — • [is]M,g = — S NP VP NP Vbe NPpred Nemo is Detdummy NC a fish x [ x  F(fish) ]<e,t>

  16. F(Nemo) <e> x [ x  F(fish) ]<e,t> Nemo is a fish • Then, as before: • [S]M,g = [VP]M,g ( [NP]M,g )= x [ x  F(fish) ] ( [NP]M,g)= x [ x F(fish) ] ( F(Nemo) )= F(Nemo) F(fish) S NP VP NP Vbe NPpred Nemo is Detdummy NC a fish x [ x  F(fish) ]<e,t>

  17. What the meaning of is is • Is is always meaningless? • It seems to be in Nemo is a fish. • But what about in Nemo is the President? Or A hungry fish is a happy fish? • The “meaningless” kind of is we’ll call predicative. The “equals” kind of is we’ll call equative.

  18. Equative be • The equative is is kind of like a conjunction that means “equals” and seems to be able to equate any two NPs. We might give the rule as (perhaps limiting a and b to NPs): • [is]M,g = b[ a [ [a]M,g = [b]M,g ] ]

  19. Nemo is a happy fish • We added a rule to allow for adjectives to attach to common nouns: • NC Adj NC • So, we should be able to draw a structure for Nemo is a happy fish.

  20. Nemo is a happy fish S ? NP VP • However, when we try to work out the truth conditions, we run into a problem. NP Vbe NPpred Nemo is Detdummy NC a Adj NC happy fish x [ x  F(happy) ]<e,t> x [ x  F(fish) ]<e,t>

  21. Nemo is a happy fish S ?<e,t> NP VP • What type should happy fish be? • Seems like it should be the same as fish. • A property (a predicate), true of individuals (<e,t>), that are happy and fish. • Nemo is happy and Nemo is a fish. NP Vbe NPpred Nemo is Detdummy NC a Adj NC happy fish x [ x  F(happy) ]<e,t> x [ x  F(fish) ]<e,t>

  22. Nemo is a happy fish S ?<e,t> NP VP • We want something that,given an individual z,is trueif happy is true of zand fish is true of z. • z [ z  F(happy)  z  F(fish) ] NP Vbe NPpred Nemo is Detdummy NC a Adj NC happy fish x [ x  F(happy) ]<e,t> x [ x  F(fish) ]<e,t>

  23. Predicate modification • To make the structure interpretable and to accomplish the desired meaning, we add a third interpretation rule: • Predicate modification[ab]M,g = z [ [a]M,g(z) [b]M,g(z) ]where a and b are predicates (type <e,t>).

  24. Predicate modification • Predicate modification[ab]M,g = z [ [a]M,g(z) [b]M,g(z) ]where a and b are predicates (type <e,t>). • For [happy fish]M,g, a will be happy, b will be fish. • [happy]M,g = x [ x  F(happy) ] • [fish]M,g = x [ x  F(fish) ] • [happy fish]M,g= z [ [happy]M,g(z) [fish]M,g(z) ]= z [ x [ x  F(happy) ](z) [fish]M,g(z) ]= z [ z F(happy) [fish]M,g(z) ]= z [ z F(happy) x [ x  F(fish) ](z) ]= z [ z F(happy) z  F(fish) ]

  25. z [ z  F(happy)  z  F(fish) ]<e,t> Nemo is ahappy fish S NP VP • Now that we have a semantic value for the whole NC, the rest proceeds as in Nemo is a fish from before. • Is and a have nosemantic value, so[NC]M,g is passed upall the way to [VP]M,g. NP Vbe NPpred Nemo is Detdummy NC a Adj NC happy fish x [ x  F(happy) ]<e,t> x [ x  F(fish) ]<e,t>

  26. z [ z  F(happy)  z  F(fish) ]<e,t> Nemo is ahappy fish F(Nemo) <e> • [S]M,g = [VP]M,g ( [NP]M,g )= z [ z  F(happy)  z  F(fish) ] ( [NP]M,g)= z [ z F(happy)  z F(fish) ] ( F(Nemo) )= F(Nemo) F(happy)  F(Nemo) F(fish) • Nemo is happy and Nemo is a fish. S NP VP NP Vbe NPpred Nemo is Detdummy NC a Adj NC happy fish

  27. (F3)

  28. The boring fish • There are two more things to add to our system before we call it complete enough for this semester. • One is to add an interpretation for the(which our syntax can generate), as in the boring fish. • The is a Det but it is different from every: It doesn’t seem to rely on the value of the sentence: • Every ab means for each x, if a is true of x, b is also true of x. • The ais just an individual, one of which a is true, with the presupposition that there is only one individual of which a is true.

  29. A unique fish • However, rather than try to incorporate presuppositions into F3, we’ll instead define the to be a quantifier like every or a except meaning a unique. • (This means not presupposing existence and uniqueness, but rather asserting it) • [the]M,g =P [ Q [ xU [P(x) y[P(y)x=y] Q(x)] ] ] • [a]M,g =P [ Q [ xU [P(x) Q(x)] ] ]

  30. The fish that Bond likes • The last thing to incorporate is the relative clause. • Idea: suppose we start with Bond likes the fish and we transform this S into an NP (the fish that Bond likes) by doing something similar to QR. • Relative clause transformation:[SX Det NCY ][NP Det [Nc NC [S that [Si [SXtiY ] ] ] ] ]

  31. Relative clause transformation NP • [that]M,g = — Det NC S NC S  … NP … that S Det NC i S … ti …

  32.         

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