A Curious Dialogical Logic and its Composition Problem

Abstract

The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. 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.

The philosophy of logical practice

“…To ensure that their proposals reflect actual research in the fields, philosophers will need to spend less time deliberating over how science and mathematics could operate given established epistemological theories and certain metaphysical assumptions about the fields, and more time looking in detail at how scientists and mathematicians actually reach their results. Much of this work will take the form of case studies, whether these be in-depth studies of the activities of an individual researcher (or research group) or wider studies of the norms within a particular sub-field (van Bendegem 2014). Historiographic studies are also commonly used, however, to trace the development of a particular prominent concept or track evolution of the methodological norms within a field (Krantz 2011), and studies from cognitive science are sometimes embraced to inform an account of how theories are evidenced or selected for (Giaquinto 2007).…”