scholarly journals C.I. Lewis, E.J. Nelson, and the Modern Origins of Connexive Logic

Organon F ◽  
2019 ◽  
Vol 26 (3) ◽  
Author(s):  
Edwin Mares ◽  
Francesco Paoli
Keyword(s):  
Connexive Logic

Relating Semantics for Connexive Logic

2020 ◽  
pp. 49-65
Author(s):  
Jacek Malinowski ◽  
Rafał Palczewski
Keyword(s):  
Connexive Logic

The Theory of Natural Consequence

Vivarium ◽  
2018 ◽  
Vol 56 (3-4) ◽  
pp. 340-366
Author(s):  
Christopher J. Martin
Keyword(s):  
Middle Ages ◽  
Fourteenth Century ◽  
Thirteenth Century ◽  
Twelfth Century ◽  
Crucial Role ◽  
Natural Consequence ◽  
History Of ◽  
Connexive Logic ◽  
Definition Of ◽  
Special Case

Abstract The history of thinking about consequences in the Middle Ages divides into three periods. During the first of these, from the eleventh to the middle of the twelfth century, and the second, from then until the beginning of the fourteenth century, the notion of natural consequence played a crucial role in logic, metaphysics, and theology. The first part of this paper traces the development of the theory of natural consequence in Abaelard’s work as the conditional of a connexive logic with an equivalent connexive disjunction and the crisis precipitated by the discovery of inconsistency in this system. The second part considers the accounts of natural consequence given in the thirteenth century as a special case of the standard modal definition of consequence, one for which the principle ex impossibili quidlibet does not hold, in logics in which disjunction is understood extensionally.

scholarly journals Rewriting the History of Connexive Logic

2022 ◽  
Author(s):  
Wolfgang Lenzen
Keyword(s):  
Twentieth Century ◽  
Classical Logic ◽  
Paraconsistent Logic ◽  
Historical Analysis ◽  
Relevance Logic ◽  
Overwhelming Majority ◽  
Lewis Carroll ◽  
Self Consistent ◽  
History Of ◽  
Connexive Logic

AbstractThe “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties (like the condition that no proposition implies its own negation) only apply to “normal” (e.g., self-consistent) antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning (“humbly”) connexive implication don’t give rise, however, to anything like a non-classical logic.

scholarly journals Axiomatization of Some Basic and Modal Boolean Connexive Logics

2021 ◽  
Author(s):  
Mateusz Klonowski
Keyword(s):  
Possible Worlds ◽  
Modus Ponens ◽  
Boolean Logic ◽  
Possible Worlds Semantics ◽  
Canonical Models ◽  
Tableau Systems ◽  
Modal Extension ◽  
Connexive Logic ◽  
Axiomatic Systems

AbstractBoolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle’s and Boethius’ theses. According to these theses (i) a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and (ii) if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.

scholarly journals Negation as Cancellation, Connexive Logic, and qLPm

2018 ◽  
Vol 15 (2) ◽  
pp. 476 ◽  
Author(s):  
Heinrich Wansing ◽  
Daniel Skurt
Keyword(s):  
Inferential Role ◽  
Original Presentation ◽  
Connexive Logic ◽  
Logic Of Paradox

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s minimally inconsistent Logic of Paradox with q-entailment (quasi-entailment) as introduced by Grzegorz Malinowski.

scholarly journals A Variant of Material Connexive Logic

2021 ◽  
Author(s):  
Alexander Belikov ◽  
Dmitry Zaitsev
Keyword(s):  
Common Sense ◽  
Informal Reasoning ◽  
Complete Axiomatization ◽  
Connexive Logic ◽  
Everyday Reasoning ◽  
The Relationship

The relationship between formal (standard) logic and informal (common-sense, everyday) reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version of connexive logic which validates Boethius' (and thus, Aristotle's) Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation.

Connexive implication

1966 ◽  
Vol 31 (3) ◽  
pp. 415-433 ◽  
Author(s):  
Storrs Mccall
Keyword(s):  
Propositional Logic ◽  
Historical Survey ◽  
Rigorous Treatment ◽  
Connexive Logic ◽  
New System

This paper contains a rigorous treatment of the species of implication described in [8] and [9], where it was given the name of connexive implication. A brief historical survey will lay bare its roots in antiquity, and it will be shown that none of the well-known systems of propositional logic serves to formalize it.1 In this paper a new system of ‘connexive’ logic will be presented, the system being shown to be (a) consistent, (b) independent of two-valued logic, (c) Post-complete.

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