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A Curious Dialogical Logic and Its Composition Problem

Uckelman, Sara L.; Alama, Jesse; Knoks, Aleks

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Authors

Jesse Alama

Aleks Knoks



Abstract

Dialogue semantics for logic are two-player logic games between a Proponent who puts forward a logical formula φ as valid or true and an Opponent who disputes this. An advantage of the dialogical approach is that it is a uniform framework from which different logics can be obtained through only small variations of the basic rules. We introduce the composition problem for dialogue games as the problem of resolving, for a set S of rules for dialogue games, whether the set of S-dialogically valid formulas is closed under modus ponens. Solving the composition problem is fundamental for the dialogical approach to logic; despite its simplicity, it often requires an indirect solution with the help of significant logical machinery such as cut-elimination. Direct solutions to the composition problem can, however, sometimes be had. As an example, we give a set N of dialogue rules which is well-justified from the dialogical point of view, but whose set N of dialogically valid formulas is both non-trivial and non-standard. We prove that the composition problem for N can be solved directly, and introduce a tableaux system for N.

Journal Article Type Article
Acceptance Date Oct 30, 2013
Publication Date Dec 1, 2014
Deposit Date Oct 7, 2014
Publicly Available Date Jul 29, 2015
Journal Journal of Philosophical Logic
Print ISSN 0022-3611
Electronic ISSN 1573-0433
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 43
Issue 6
Pages 1065-1100
DOI https://doi.org/10.1007/s10992-013-9307-1
Keywords Composition problem, Dialogical logic, Tableaux.
Public URL https://durham-repository.worktribe.com/output/1422283

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