So, the semantic type of an adjective can be either <e, t> or <<e, t>, <e, t>>?

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1 1 Semantics I April 16 Lambda and Relative Clause Adjectives Two ways to combine an adjective and a noun red book (1) via Functional Application: Px[red'(x) P(x)]y[book'(y)]) = x[red'(x) y[book'(y)](x)] = x[red'(x) book'(x)] <e, t> Px[red'(x) P(x)] y[book'(y)] <<e, t>, <e, t>> <e, t> (2) via Generalized Conjunction (a.k.a. variable identification): x[red'(x) book'(x)] <e, t> x[red'(x)] y[book'(y)] <e, t> <e, t> So, the semantic type of an adjective can be either <e, t> or <<e, t>, <e, t>>? Adjective of the type <e, t> is predicative. (3) This book is red. Adjective of the type <<e, t>, <e, t>> is strictly prenominal. (4) This is a red book. Some adjectives are not predicative. (5) a. John is a former teacher. b. *John is former. (6) a. John is an alleged thief. b. *John is alleged.

2 2 Nonpredicative adjectives are always <<e, t>, <e, t>>. Other adjectives, such as red, round, blond, etc. can be either <e, t> or <<e, t>, <e, t>>, but if generalized conjunction is available, then these adjectives might as well be just <e, t>. So we could say that there are two sets of adjectives with different types: - <e, t> (red, round, blond, etc.) - <<e, t>, <e, t>> (former, alleged, etc.) Or, we could also say that all adjectives are of the type <<e, t>, <e, t>>; they type-shift whenever necessary. (We ll look at different types of NPs and type-shifting principles next week) c.f. Another kind of adjective classification (Kamp and Partee, 1995; Partee, 1995) (7) a. Intersective adjectives: red, blond, rectangular, French, etc. [[red N]] = [[red]] [[N]] b. Subsective adjectives: skillful, typical, recent, perfect, etc. [[skillful N]] [[N]] c. Non-subsective adjectives: former, alleged, questionable, potential, etc. [[former N]] [[former]] [[N]] [[former N]] [[N]] d. Privative adjectives: fake, counterfeit, imaginary, fictitious, etc. [[fake N]] [[N]] = Relative clauses Introduction A relative clause is a predicate derived from a sentence. Deriving a predicate from a sentence is essentially what the lambda operator is designed to do. (8) a. a teacher whom Mary likes b. the woman who lives next door Restrictive relative clauses are like adjectives. They involve predicate conjunction (i.e. set intersection). cf. Restrictive vs. non-restrictive relative clause (9) a. The train that arrived at 11 was behind schedule. (restrictive) b. The train, which arrived at 11, was behind schedule. (non-restrictive) Restrictive, like adjectives are predicate conjunction: (10) x[train'(x) arrived.at.11'(x)] Non-restrictive is like sentential conjunction: (11) [The train arrived at 11] [The train was behind schedule]

3 3 Back to restrictive relative clauses One analysis: (12) a teacher whom Mary likes NP Det N <e, t> y[teacher'(y) like'(mary', y)] (generalized conjunction) a N <e, t> CP <e, t> x i [like'(mary', x i )] teacher whom i C y[teacher'(y)] C S t like'(mary', x i ) that NP e VP <e, t> Mary V <e, <e, t>> NP e likes e i like'(mary', x i ) xlike'(mary', x i ) This is the same type-shift we saw for quantifiers, although this time it has a possible overt reflex (i.e. the relative pronoun). At PF, either the complementizer or the relative pronoun is deleted. Above is the analysis presented in the textbook but there is no problem adopting the following syntax instead. (13) a. a teacher [ CP whom i [ IP Mary likes e i ]] b. a teacher [ CP OP i that [ IP Mary likes e i ]] c.f. Complementizer contraction for subject relative (14) a. This is the letter [ CP OP i that [ IP e i will surprise Poirot]]. b. This is the letter [ CP that i [ IP e i will surprise Poirot]]. In (14a), the trace in the subject position cannot be properly governed by its antecedent because of the intervening C. Pesetsky (1982) proposes a special coindexation mechanism to account for the grammaticality. The empty operator and the complementizer are collapsed into one constituent which has all the relevant features of the operator.

4 4 Quantifiers (15) a. [[every teacher]] Px[teacher'(x) P(x)] b. [[some teacher]] Px[teacher'(x) P(x)] c. [[a teacher]] Px[teacher'(x) P(x)] d. [[three teachers]] Px[teacher'(x) P(x)x 3] <<e, t>, t> (16) a. [[every]] QPx[Q(x) P(x)] b. [[some]] QPx[Q(x) P(x)] c. [[a]] QPx[Q(x) P(x)] d. [[three]] QPx[Q(x) P(x)x 3] <<e, t>, <<e, t>, t>> Back to the tree: NP <<e, t>, t> Px[teacher'(x) like'(mary', x) P(x)] Det <<e, t>, <<e, t>, t>>> N <e, t> y[teacher'(y) like'(mary', y)] a N <e, t> CP <e, t> x[like'(mary', x i )] QPx[Q(x) P(x)] teacher y[teacher'(y)] References: Haegeman, Liliane Introduction to Government and Binding Theory. Oxford: Blackwell. Kamp, Hans, and Barbara Partee Prototype theory and compositionality. Cognition 57: Partee, Barbara. (1995). Lexical semantics and compositionality. In An Invitation to Cognitive Science (Second Edition). Volume 1: Language, eds. Lila Gleitman and Mark Liberman, Cambridge: MIT Press. Pesetsky, David Complementizer-trace Phenomena and the Nominative Island Condition. The Linguistic Review 1:

5 5 Homework 8 Give the derivations (syntax, semantics) of 1. a girl who has three books 2. Every man loves a girl who has three books. Since the complete tree for (2) will get enormous, treat [ NP a girl who has three books] as a single chunk in (2). Instead, give a full analysis of the NP in (1). For your reference, here s what we went over before the spring break: John loves every woman TP Px[woman'(x) P(x)](x i [love'(j, x i )]) = x[woman'(x) x i [love'(j, x i )] (x)] = x[woman'(x) love'(j, x)] every woman i TPx[love'(x, x i )](j) = love'(j, x i ) x i [love'(j, x i )] Px[woman'(x) P(x)] John VP y[x[love'(x, y)]](x i ) = x[love'(x, x i )] John' loves e i yx[love'(x, y)] x i