1 Semantics in Generative Grammar Angelika Kratzer September 17, 2007 1. A semantics with events In addition to the basic domains De and Dt, we have a domain Ds, the domain of (actual) events. We adjust Definition 5 on p. 28 of Heim & Kratzer accordingly: Semantic Types (a) e, t, and s are semantic types. (b) If and are semantic types, then < > is a semantic type. (c) Nothing else is a semantic type. Semantic denotation domains (a) De = D = the set of individuals. (b) Dt = {0,1} = the set of truth-values. (c) Ds = E = the set of events. (d) For any semantic types and , D<, > is the set of all functions from D to D . Examples of lexical meaning assignments: [[dance]] D<e<st>>. For all a D and e Ds, [[dance dance]](a)(e) = 1 iff e is an event of dancing by a. [[cross]] D<e<e<st>>>. For all a and b D and e Ds, [[cross]](b)(a)(e) = 1 iff e is an event of crossing b by a. Consequence Small clauses like Mary dance or Mary cross Main Street might now be taken to denote (characteristic functions of) sets of events.2 (1) Bea saw Josie dance. (2) Bea saw Josie cross Main Street. (3) Bea made Josie dance. (4) Bea made Josie cross Main Street. 2. Class exercises a. Write down the denotations of dance and cross in the informal -notation of Heim & Kratzer. What are the semantic types of those denotations? b. Draw suitable phrase structure trees for the small clauses in (1) and (2), and compute the denotation of the tree node by node. c. Draw a tree for (5) below, giving the tense morpheme scope over the rest of the sentence. Write down a possible denotation for the tense morpheme in the informal -notation of Heim & Kratzer. What is the semantic type of the tense morpheme? Compute the denotation of (5), step-by-step, recycling the piece you computed already. (5) Josie danced. d. Can you think of a possible denotation for the verb roots see and (causative) make as used in (1) to (4)? What would be their semantic type? Draw a suitable tree, write down possible denotations for see and make in the informal -notation of Heim & Kratzer. Then compute the denotation of (1) step-by-step, recycling pieces you computed
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