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A curious dialogical logic and its composition problem.

Uckelman, Sara L. and Alama, Jesse and Knoks, Aleks (2014) 'A curious dialogical logic and its composition problem.', Journal of philosophical logic., 43 (6). pp. 1065-1100.

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.

Item Type:Article
Keywords:Composition problem, Dialogical logic, Tableaux.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1007/s10992-013-9307-1
Publisher statement:The final publication is available at Springer via http://dx.doi.org/10.1007/s10992-013-9307-1.
Date accepted:30 October 2013
Date deposited:29 July 2015
Date of first online publication:December 2014
Date first made open access:No date available

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