A logical account of questions

Raboczi, Simon (2013). A logical account of questions PhD Thesis, School of Information Technology and Electrical Engineering, The University of Queensland.

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Author Raboczi, Simon
Thesis Title A logical account of questions
Formatted title
A Logical Account of Questions
School, Centre or Institute School of Information Technology and Electrical Engineering
Institution The University of Queensland
Publication date 2013-01-01
Thesis type PhD Thesis
Supervisor Guido Governatori
Robert Colomb
Total pages 119
Total colour pages 12
Total black and white pages 107
Language eng
Subjects 080203 Computational Logic and Formal Languages
220308 Logic
010107 Mathematical Logic, Set Theory, Lattices and Universal Algebra
Formatted abstract
This thesis describes two conservative extensions to the language of rst order logic (FOL) to allow the represention of questions as well as propositions. It is motivated by an interest in formal query languages for information systems.

    The key idea employed is a particular semantic denition of \question". The semantics used is based on possible worlds. Propositions can be represented in the manner familiar from modal logics, as the set of possible worlds in which they happen to be true. The philosophical literature on question logics supports (albeit not without dispute) the notion that questions are equivalent to the set of their answers, and the notion that the answers to a question are asserted propositions. Combining these premises gives rise to the denition that a question is a set of sets of possible worlds.

    The two levels of set in this representation of questions can be exploited in a systematic way. The two levels each feature a subset relation. The subset relation between the inner sets (of worlds) corresponds to the conventional semantic relation of propositional entailment in FOL. The subset relation between the outer sets (of propositions) corresponds to the semantic relation of question containment from the question logic literature. This structural similiarity allows a workable logic of questions to be created by taking the machinery of classical predicate logic which applies to the inner subset relation between propositions, and creating a mirror version of it to deal with the outer subset relation between questions.

    This mirroring is performed by extending the syntax of FOL with a question forming counterpart for each of the familiar connectives and quantiers. The two most important additions are a counterpart to the disjunction connective, which forms questions about the truth of various propositions such as \whether or not X", and a counterpart to existential quantication, which forms questions about individuals such as \what are the Xs". Counterparts to the natural deduction rules for each connective and quantier are used to produce a sound proof system.

    A further conceptual simplication is considered, that of considering propositions as the singleton case of questions. This allows the previous two-typed language of propositions and questions to be reduced to a single-typed language of questions alone. The grammar and semantics propositional connectives and quantiers is extended from the previous language so that they have a sensible denition when applied to questions. The model theory for the single-typed language was implemented as a Java program and used to confirm the validity of a test suite of entailments and equivalences on small nite models.
Keyword Erotetics
Logic of questions

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Created: Tue, 23 Jul 2013, 08:12:33 EST by Mr Simon Raboczi on behalf of Scholarly Communication and Digitisation Service