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King’s College London This paper is part of an examination of the College counting towards the award of a degree. Examinations are governed by the College Regulations under the authority of the Academic Board. MA EXAMINATION 7AAN2092 Theory of Meaning Examination Period 2 (May 2015) TIME ALLOWED: 2 HOURS Answer ONE question from Section A and ONE question from Section B. Avoid overlap in your answers. DO NOT REMOVE THIS PAPER FROM THE EXAMINATION ROOM TURN OVER WHEN INSTRUCTED 2015 © King’s College London 7AAN2092 Section A 1. (a) What do the basic types e and t represent? (b) What is the semantic type of a transitive verb? (c) Give a recursive definition of the domain of interpretation of types. (d) What is the domain of the type (e → t) → (e → t)? (e) Give an example of a word which would be naturally modeled with a constant of type (e → t) → (e → t) and describe the denotation of that constant. (f) Assign types to the following words: i. ii. iii. iv. v. vi. John every cat cuddles violently student (g) Using the type assignments given in (f), show that the sentence “John violently cuddles every cat.” has type t (h) The notion of semantic consequence is defined in type theory, but not the notion of syntactic consequence. Explain this absence. 2. (a) Define α, β and η reduction. (b) When is α-reduction necessary? Give an example of an expression which requires α-reduction to be normalized. (c) Normalise these expressions, showing each step that you take. i. (λP.P (likes))(λQ.Q(j)) ii. (λx.λy(likes)(y)(x))(john) (d) Define [[λx.α]] with respect to a model M and variable assignment g. (e) Argue that β-reduction is sound. Sketch a proof. 3. (a) What is the role of intensional types in formal semantics? (b) Give a definition of the set of types used in intensional logic. (c) Define the syntax and semantics of the intensional operators ∨ . ∧ and (d) Give an example of sentences where the intensional operators ∨ are used. ∧ and (e) Are ∧∨ α and ∨∧ α always equivalent to α? Explain your answers. 2 TURN OVER 7AAN2092 Section B 4. What are the advantages and limitations of representing the meaning of a proposition as a function from possible worlds to truth values? 5. Discuss the limitations of First-Order Logic as a representation language for natural languages, and how they can be overcome using higher-order logic. 6. Discuss the role of meaning postulates in Montague semantics. 7. How is a uniform treatment of noun-phrases obtained in Montague semantics? Explain how this could be applied to the phrase “John and every dog”. 3 END OF PAPER