First-Order Dialogical Games and Tableaux

Clerbout, Nicolas

doi:10.1007/s10992-013-9289-z

Cited by 38 publications

(15 citation statements)

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“…Indeed, Felscher himself envisaged dialogues characterizing classical logic without the E rule (in [10, §3.10] he briefly considers so-called Cdialogues in which the E rule is not available). Recent results show that E need not be assumed for the purpose of characterizing classical logic using dialogues [6,40]. In [6], Clerbout uses a slightly different notion of dialogues (in effect, he works with a different class of structures) in which the notion of rank -numeric bounds on the number of repetitions the players are permitted-ensures that all dialogues whatsoever are finite, whereas Uckelman in [40] shows that, for Felscher dialogues, all that is necessary to obtain classical logic is to limit the number of repetitions that Opponent may make.…”

Section: Resultsmentioning

confidence: 99%

“…10], certain paraconsistent logics [32], approximated logics [13, p. 210], and indeed, nonmonotonic logics in general. 6 Even if one were to insist on the presence of unrestricted uniform substitution, there are logics whose dialogical characterizations do not validate unrestricted uniform substitution, such as connexive logic [26], [34, §4.2] and relevance logic [34, §3.3].…”

Section: The Composition Problemmentioning

confidence: 99%

“…1]. 6 One can think of logics which do not satisfy unrestricted uniform substitution as being propositional theories, where the interpretation of the atomic variables is fixed in advance. 7 In many logics, it doesn't make sense to distinguish a schematic/substitutional notion of consequence from a non-substitutional one.…”

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confidence: 99%

“…1,6]; for a dialogical characterization of linear logic, see [4]. 12 More precisely, we attach to the end of f (b) the result of cutting off the root of t, because the root of t and the leaf of b represent assertions by P of identical formulas.…”

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A Curious Dialogical Logic and its Composition Problem

2013

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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.

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Section: Resultsmentioning

confidence: 99%

Section: The Composition Problemmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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A Curious Dialogical Logic and its Composition Problem

2013

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“…Une des particularités du cadre dialogique est de remplacer la sémantique "dénotationnelle", c'est-à-dire une théorie du sens qui projette le sens des expressions et des opérations en externe via une théorie de la dénotation 2 , par une sémantique "opérationnelle", où le sens est généré en interne par des paires de mouvements : un challenge et une défense. Ainsi, le sens d'un opérateur logique, c'est qu'il peut être mis en question d'une certaine manière, mise en question à laquelle on peut répondre ou on ne peut pas répondre, d'une certaine manière.…”

Section: Règles Des Particulesunclassified

Dialogique des matrices

Cardascia

2015

RHV

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RésuméLa logique dialogique ordinaire propose un traitement de la mémoire sous la forme d'un historique des dialogues. Rechercher une référence (la justification) dans cet historique est un processus ambiguë en cas de répétition, ce qui peut rendre complexes ou impossibles les questions de composition de dialogue. Ainsi, deux recherches de justification peuvent se superposer en une double justification problématique. De plus, ce traitement de la mémoire coûte techniquement beaucoup de ressources.Nous proposons un formalisme de la dialogique qui résout ces problèmes: double-justification, composition, économie de mémoire. Pour ce faire, nous internaliserons des règles analysées comme "spéciales", reconfigurant en grande partie le formalisme et à sa suite les notions philosophiques voire métaphysiques mises en jeu dans ce système logique et dans ses interprétations.Cet article se découpe en trois parties :1. Une présentation du cadre dialogique orientée vers la présentation du problème de la double justification.2. Une ré-interprétation de ce cadre en termes de matrices : les formules logiques calquées sur la lecture linguistico-mathématique du langage sont remplacées par un concept emprunté à la game semantic, celui de position (sous la forme de matrices de formules).3. Une brève synthèse des nouvelles perspectives offertes par cette méthode : réaffirmation de la séparation claire entre les différents niveaux d'analyse et économie sur la quantité de mémoire requise (payée en complexité).

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Dialogues, Reasons and Endorsement

Rahman

2019

Constructive Semantics

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The main aim of the present paper is to show that, if we follow the dialogical insight that reasoning and meaning are constituted during interaction, and we develop this insight in a dialogical framework for Martin-Löf's Constructive Type Theory, a conception of knowledge emerges that has important links with Robert Brandom's (1994 inferential pragmatism. However, there are also some significant differences that are at center of the dialogical approach to meaning. The present paper does not discuss explicitly phenomenology, however, one might see our proposal as setting the basis for a further study linking phenomenology and the dialogical conception of meaningthe development of such a link is part of several ongoing researches. I Shahid Rahman 2 2 Local reasonsRecent developments in dialogical logic show that the Constructive Type Theory approach to meaning is very natural to the game-theoretical approaches in which (standard) metalogical features are explicitly displayed at the object language-level. 3 This vindicates, albeit in quite a 2 In fact, the present paper relies on the main technical and philosophical results of Rahman/McConaugey/ Klev/Clerbout (2018). 3 Such as developed in Rahman/McConaugey/Klev/Clerbout (2018) and also in Clerbout/Rahman (2015). different fashion, Hintikka's plea for the fruitfulness of game-theoretical semantics in the context of epistemic approaches to logic, semantics, and the foundations of mathematics. 4 From the dialogical point of view, the actions-such as choices-that the particle rules associate with the use of logical constants are crucial elements of their full-fledged (local) meaning: if meaning is conceived as constituted during interaction, then all of the actions involved in the constitution of the meaning of an expression should be made explicit; that is, they should all be part of the object-language.This perspective roots itself in Wittgenstein's remark according to which one cannot position oneself outside language in order to determine the meaning of something and how it is linked to syntax; in other words, language is unavoidable: this is his Unhintergehbarkeit der Sprache. According to this perspective of Wittgensteins, language-games are supposed to accomplish the task of studying language from a perspective that acknowledges its internalized feature. This is what underlies the approach to meaning and syntax of the dialogical framework in which all the speech-acts that are relevant for rendering the meaning and the "formation" of an expression are made explicit. In this respect, the metalogical perspective which is so crucial for model-theoretic conceptions of meaning does not provide a way out. It is in such a context that Lorenz writes:Also propositions of the metalanguage require the understanding of propositions, […] and thus cannot in a sensible way have this same understanding as their proper object. The thesis that a property of a propositional sentence must always be internal, therefore amounts to articulating the insight that in propositions about ...

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First-Order Dialogical Games and Tableaux

Cited by 38 publications

References 7 publications

A Curious Dialogical Logic and its Composition Problem

A Curious Dialogical Logic and its Composition Problem

Dialogique des matrices

Dialogues, Reasons and Endorsement

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