Syntax 1 Wiki: Week 3

Valence

Exercise 1 For I(cat¹) and I(lilly), specify one plausible value each so that the formula cat¹(lilly) becomes true in M.

Check your answer

I(cat¹) = {<cat1>,<cat2>,<cat3>}

For I(lilly), each of the following 3 values will now make cat¹(lilly) true in M:
a. I(lilly) = cat1 , or
b. I(lilly) = cat2 , or
c. I(lilly) = cat3 .

We prove this for case (b):

1. [[cat¹(lilly)]]^M = 1 iff <[[lilly]]^M> ∈ I(cat¹)
2. iff <I(lilly)> ∈ I(cat¹)
3. iff <cat2> ∈ {<cat1>,<cat2>,<cat3>}

Hence: since (3) is the case, so are (2) and the righthand side of (1). Finally, since the righthand side of (1) is the case, the lefthand side is the case as well. Hence [[cat¹(lilly)]]^M is true in model M. That is what we intended to prove!

1. Kim snores.

1. Kim snores.

2. Kim likes Robin.
3. Kim talked to the student.
4. Kim showed Hessen to Robin.
5. Kim handed Robin the apple.

1. Amid the incessant crackle of gunfire , the soldiers usher the cowering men through darkened rooms .

Example	SUBJ	COMPS
snores	<NP[nom]>	<>
likes	<NP[nom]>	<NP[acc]>
put[base]	<NP>	<NP[acc],PP>
persuade[base]	<NP>	<NP[acc],VP[inf]>
afraid	<NP>	<PP>
of	<>	<NP[acc]>
that (C)	<>	<S[fin]>

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