3: Axiomatizing Groenendijk's Logic of Interrogation
In: Questions in Dynamic SemanticsSearch for other papers by Balder ten Cate in
Current site
Google Scholar
PubMed
Search for other papers by Chung-Chieh Shan in
Current site
Google Scholar
PubMed
Purchase instant access (PDF download and unlimited online access):
Abstract
Jeroen Groenendijk introduced a logic, which he called the Logic of Interrogation (LoI), that can be used to analyze which linguistic answers are appropriate in response to a given question. Groenendijk gave only a semantic definition of his logic. For practical applications like building question-answering systems, understanding of the proof theory of this logic is needed. This chapter bridges this gap by providing a sound and complete axiomatization for Lol. It presents a connection between entailment in LoI and Beth's definability theorem for first-order logic. The chapter explains how LoI can be seen not only as a logic for reasoning about linguistic questions and answers, but also with natural interpretations in mathematics, database theory, and philosophical logic. Finally, it shows not only a natural linguistic interpretation, but also describes equivalence relations between models, reductions among database queries, and logicality of operations.