A Curious Dialogical Logic and its Composition Problem

Journal of Philosophical Logic 43 (6):1065-1100 (2014)
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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.

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Author Profiles

Sara L. Uckelman
Durham University
Aleks Knoks
University of Luxembourg

Citations of this work

The philosophy of logical practice.Ben Martin - 2022 - Metaphilosophy 53 (2-3):267-283.
Dialogical logic.Laurent Keiff - 2010 - Stanford Encyclopedia of Philosophy.
A Curious Dialogical Logic and its Composition Problem.Sara L. Uckelman, Jesse Alama & Aleks Knoks - 2014 - Journal of Philosophical Logic 43 (6):1065-1100.
A dialogical route to logical pluralism.Rohan French - 2019 - Synthese 198 (Suppl 20):4969-4989.

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Connexive implication.Storrs Mccall - 1966 - Journal of Symbolic Logic 31 (3):415-433.

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