Questions require an answer: A deductive perspective on questions and answers

Proceedings of the 2006 Australasian Language Technology Workshop (ALTW2006), pages 107–114. Questions require an answer: A deductive perspective on questions and answers Willemijn Vermaat Centre for Logic, Language and Computation Victoria University Wellington, New Zealand vermaat@mcs.vuw.ac.nz Abstract Direct questions such as “Who saw Mary?” intuitively request for a certain type of answer, for instance a noun phrase “John” or a quantified noun phrase such as “A man”. Following the structured meaning approach to questions, we pro- pose an analysis of wh-questions in type- logical grammar that incorporates the re- quirement for a certain type of answer into the type assigned to wh-phrases. Inter- estingly, the syntactic and semantic de- composition leads to a derivability pattern between instances of wh-phrases. With this pattern we can explain the differ- ence between wh-pronouns (‘who’) and wh-determiners (‘which’), and derive wh- questions that require multiple answers. 1 Introduction In this paper, we discuss the uniform basis of dif- ferent types of wh-questions focusing on the de- pendency relation between questions and answers. In loose terms, a wh-question can be interpreted as a sentence which still requires an answer. The answer to a question such as “‘Who saw Mary?” serves as an argument of the main or embedded verb clause. In more formal terms, the meaning assembly of the above wh-question may be repre- sented by the lambda term, λx.((see m) x). We show that by incorporating the dependency rela- tion between questions and answers into the lexi- cal type-assignments of wh-phrases, wh-questions can be instantiated in an uniform way. Section 2 gives a short introduction in type- logical grammar and introduces the basic setup of the grammatical reasoning system. In section 3, we briefly discuss two approaches to the semantics of questions: the proposition set approach and the structured meaning approach. Section 4 provides the syntactic and semantic type of wh-questions and introduces a wh-type schema to identify wh- phrases. Additionally, we show how meaning as- sembly for wh-questions is derived on the basis of a structured meaning approach to questions and answers. In section 5, we show how we can de- rive type alternations for wh-phrases which lead to derivability schemata between instances of wh- type schema. Finally, in section 6, we analyze dif- ferent types of question-answer combinations and multiple wh-questions in English on the basis of these derivability schema. We finish with the con- clusion and some pointers for future research. 2 Type-logical grammar Type-logical grammar (Moortgat, 1997) offers logical tools that can provide an understanding of both the constant and the variable aspects of lin- guistic form and meaning.1 Type-logical gram- mar is a strongly lexicalised grammar formalism, which, in the case of a categorial system, means that a derivation is fully driven by the types as- signed to lexical elements: these types are the ba- sic declarative units on which the computational system acts. The basis for the type system is a set of atomic or basic types. The full set of types is then built out of these …

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