Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 1 Midterm Exam You have until Monday, November 7th to complete the questions below. Some of these questions can be answered very quickly, while others will require more thought (and writing). Please bear this in mind when planning how to make the most effective use of your time. You may talk with me in person or over e-mail about any questions you might have on any of these problems (within reason). You are also free to consult with others, but each person is responsible for writing up their own distinct answers. 1) Some Questions on the Conceptual Foundations of the Field a. What is the ‘principle of compositionality’? Why do we think it is true? b. In a few sentences, please explain the intellectual value of a formal system that can derive the truth-conditions of every (declarative) sentence of some natural language. c. If a person asserts the sentence in (i), we usually infer the proposition in (ii). (i) Dave has read every book that Kim Kardashian has written. (ii) Kim Kardashian has written at least one book. Is the proposition in (ii) part of the asserted content of (i), and why or why not? Is it a presupposition of (i), and why or why not? Is it an implicature of (i), and why or why not? 2) A Synthesis of All That We’ve Learned Thus Far Consider the dialog in (a) below. Person 2’s utterance can be observed to have the asserted content in (b), the presuppositions in (c), and the implicature in (d). a. Person 1: Which of Dave’s paintings did the old women sell? Person 2: The picture which he painted, the old woman sold. b. Asserted Content of Person 2’s Utterance The unique x such that x is a woman and x is above average age for women sold the unique y such that y is a picture and Dave painted y. c. Presuppositions of Person 2’s Utterance 1. There is exactly one x in the context such that x is a woman and x is above average age for a woman. 2. There is exactly one y in the context such that y is a picture and Dave painted y. d. Implicature of Person 2’s Utterance The old woman sold no other paintings of Dave’s.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 2 e. Exercise 1: Please show how our extensional semantics predicts that Person 2’s utterance has the asserted content in (2b). Assume that it has the syntax below. S’’ DP3 S’1 D3 NP3 3 S1 the NP3 CP DP4 VP1 N3 DP1 S’2 D NP4 V1 t3 picture D1 1 S2 the AP NP4 sold which1 DP2 VP2 A N4 GEN D2 V2 t1 old woman MASC PRO2 painted f. Exercise 2: Please explain how our extensional semantics predicts that Person 2’s utterance has the presuppositions in (2c). g. Exercise 3: Please show how the classic, Gricean theory of implicatures accounts for the implicature in (2d). h. Exercise 4: There is no imaginable context where Person 2’s utterance could have the following as its asserted content: “The unique x such that x is a woman and x is above average age for women sold the unique y such that y is a picture and Mary painted y.” Explain how this is predicted by our semantics for pronominal gender.Seth Cable Semantics and Generative Grammar Fall 2011 Ling610 3 3) An Initial Foray into Plural NPs Consider the sentence “Frank and Dave are boys”, which we will assume to have the syntax below. a. S DP3 VP DP1 ConjP V NP4 D1 NP1 Conj DP2 are N4 PLURAL ∅ N1 and D2 NP2 boy s Frank ∅ N2 Dave b. Question 1: Assume that the copula are has the same extension as the copula is in a sentence like “Dave is a boy.” What, then, must be the semantic type of “PLURAL”? Let us now expand our concept of ‘entity’ so that it includes so-called ‘groups’ of entities. For any two entities x and y, there is also the ‘group’ consisting of x and y, which we will write as ‘x+y’. For example, Rajesh+Seth would be the ‘group’ consisting of Rajesh and Seth, and Rajesh+Seth+Shayne would be the ‘group’ consisting of Rajesh, Seth and Shayne. Finally, both Rajesh+Seth and Rajesh+Seth+Shayne would count as ‘entities’, and so be members of De. c. Question 2: Please provide a lexical entry for and in (3a) so that [[DP3]] = Frank+Dave. What would be the semantic type of this version of “and”? d. Question 3: Please provide a lexical entry for ‘PLURAL’ that will predict the following truth-conditions for (3a): [[ (3a) ]] = T iff Frank+Dave is a group formed from the members of { x : x is a boy } e. Question 4: Consider the sentence “the boys smoke”. Given your answer to Question 3, will our semantic system be able to interpret this sentence? If so, what T-conditions does it assign? If not, why