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Durham University

Institute of Medieval and Early Modern Studies (IMEMS)

Members

The list below shows Durham University research staff who are members of IMEMS. Click the member's name to see a more detailed biography and department.

We also welcome anyone from outside the University with an interest in our work to join. Membership is free of charge. You will receive invitations to our programme of events, with a weekly emails digest about what is happening in the Insitute and further afield. To join IMEMS contact: admin.imems@durham.ac.uk

Publication details for Dr Sara L. Uckelman

Uckelman, Sara L., Alama, Jesse & Knoks, Aleks (2014). A Curious Dialogical Logic and Its Composition Problem. Journal of Philosophical Logic 43(6): 1065-1100.

Author(s) from Durham

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.