Intuitionistic Logic is a Connexive Logic

Fazio, Davide; Ledda, Antonio; Paoli, Francesco

doi:10.1007/s11225-023-10044-7

Cited by 5 publications

(2 citation statements)

References 48 publications

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“…A suggestive concrete example of conditional of the kind encoded by ⇒ 2 might be the following: "x is the only reason justifying y". Note that a connexive implication with a similar reading has been proposed by [10] within the framework of Semi-Heyting algebras.…”

Section: Weakly Connexive Implications and Relevancesupporting

confidence: 66%

Some Remarks on the Logic of Probabilistic Relevance

Fazio,

Mascella

2023

LLP

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In this paper we deepen some aspects of the statistical approach to relevance by providing logics for the syntactical treatment of probabilistic relevance relations. Specifically, we define conservative expansions of Classical Logic endowed with a ternary connective ⇝ - indeed, a constrained material implication - whose intuitive reading is “x materially implies y and it is relevant to y under the evidence z”. In turn, this ensures the definability of a formula in three-variables R(x, z, y) which is the representative of relevance in the object language. We outline the algebraic semantics of such logics, and we apply the acquired machinery to investigate some termdefined weakly connexive implications with some intuitive appeal. As a consequence, a further motivation of (weakly) connexive principles in terms of relevance and background assumptions obtains.

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Section: Weakly Connexive Implications and Relevancesupporting

confidence: 66%

Some Remarks on the Logic of Probabilistic Relevance

Fazio,

Mascella

2023

LLP

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“…Davide Fazio, Antonio Ledda, and Francesco Paoli [6] have shown that a connexive implication, that we will denote with the symbol '→ c ', can be defined within intuitionistic logic by putting…”

Section: Connexive Implication Within Intuitionistic Logicmentioning

confidence: 99%

Constructive Logic is Connexive and Contradictory

Wansing

2024

LLP

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It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan’s drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent).

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On the Provable Contradictions of the Connexive Logics C and C3

Niki

Wansing

2023

J Philos Logic

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Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3.

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Intuitionistic Logic is a Connexive Logic

Cited by 5 publications

References 48 publications

Some Remarks on the Logic of Probabilistic Relevance

Some Remarks on the Logic of Probabilistic Relevance

Constructive Logic is Connexive and Contradictory

On the Provable Contradictions of the Connexive Logics C and C3

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