A multi-type calculus for inquisitive logic

Conference paper (2016)

Authors

S.S.A. Frittella Ethics & Philosophy of Technology - TPM
G. Greco Ethics & Philosophy of Technology - TPM
A. Palmigiano Ethics & Philosophy of Technology - TPM
F. Yang Ethics & Philosophy of Technology - TPM
Research Group
Ethics & Philosophy of Technology (TPM) (TU Delft)
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Published Date

2016

Language

English

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Faculty

Technology, Policy and Management

Department

Values Technology and Innovation

Research Group

Ethics & Philosophy of Technology

Abstract

In this paper, we define a multi-type calculus for inquisitive logic, which is sound, complete and enjoys Belnap-style cut-elimination and subformula property. Inquisitive logic is the logic of inquisitive semantics, a semantic framework developed by Groenendijk, Roelofsen and Ciardelli which captures both assertions and questions in natural language. Inquisitive logic adopts the so-called support semantics (also known as team semantics). The Hilbert-style presentation of inquisitive logic is not closed under uniform substitution, and some axioms are sound only for a certain subclass of formulas, called flat formulas. This and other features make the quest for analytic calculi for this logic not straightforward. We develop a certain algebraic and order-theoretic analysis of the team semantics, which provides the guidelines for the design of a multi-type environment accounting for two domains of interpretation, for flat and for general formulas, as well as for their interaction. This multi-type environment in its turn provides the semantic environment for the multi-type calculus for inquisitive logic we introduce in this paper.