Connexive implication

McCall, Storrs

doi:10.2307/2270458

Cited by 82 publications

(49 citation statements)

References 5 publications

(7 reference statements)

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“…A usual mistake is to interpret ancient logics based on standard logic (for arguments in this sense for Stoic logic, see, e.g., Bobzien, 1996, p. 134;or López-Astorga, 2016c, p. 22) and maybe those logics require to be understood in their contexts. Thus, in the particular case of Boethius' inference, it can be thought, as held by McCall (1966), that Boethius did not accept Philo's interpretation of the conditional, but that he assumed Chrysippus' criterion of it, which is to be found in many texts written by both ancient and contemporary authors (e.g., Cicero, De Fato 12; Diogenes Laërtius, Vitae Philosophorum 7, 73; Sextus Empiricus, Pyrrhoniae Hypotyposes 2, 111; Barnes, Bobzien, & Mignucci, 2008, p. 107;Gould, 1970, p. 76;López-Astorga, 2015b, p. 9, 2016dMueller, 1978, p. 20;O'Toole & Jennings, 2004, p. 479). Based on them, it can be stated that, following Chrysippus of Soli, a conditional is only correct when the denial of its then-clause is in contradiction with its if-clause.…”

Section: Discussionmentioning

confidence: 97%

The Problem of the Negation of the Conditional

Astorga¹

2017

rupkatha

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People usually seem to negate the conditional in a different way as it is provided by standard logic. Both contemporary experimental results and texts coming from ancient sources appear to demonstrate that individuals tend not to negate the conditionals in entirety, but only their consequents. Obviously, this can lead one to think that there is no relationship between standard logic and human language and reasoning. However, in this paper, I try to show that, in spite of the mentioned results and texts, it is possible to continue to accept that there are certain links between systems such as that of Gentzen and the way people often negate the conditionals. That way is not, in many cases, exactly the one required by standard logic, but it is not absolutely inconsistent with the latter either.

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Section: Discussionmentioning

confidence: 97%

The Problem of the Negation of the Conditional

Astorga¹

2017

rupkatha

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“…Schemata (AT1) and (AT2) are often referred to as Aristotle's theses [6]. Some logicians characterize connexive systems in terms of stronger versions of Boethius' theses which we will not discuss here.…”

Section: Systems Of Conditional Logicmentioning

confidence: 99%

Connexive Extensions of Regular Conditional Logic

Weiss

2018

LLP

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Abstract. The object of this paper is to examine half and full connexive extensions of the basic regular conditional logic CR. Extensions of this system are of interest because it is among the strongest well-known systems of conditional logic that can be augmented with connexive theses without inconsistency resulting. These connexive extensions are characterized axiomatically and their relations to one another are examined proof-theoretically. Subsequently, algebraic semantics are given and soundness, completeness, and decidability are proved for each system. The semantics is also used to establish independence results. Finally, a deontic interpretation of one of the systems is examined and defended.

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“…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%

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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Connexive implication

Cited by 82 publications

References 5 publications

The Problem of the Negation of the Conditional

The Problem of the Negation of the Conditional

Connexive Extensions of Regular Conditional Logic

A Curious Dialogical Logic and its Composition Problem

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