An Epistemic Interpretation of Paraconsistent Weak Kleene Logic

Szmuc, Damián Enrique

doi:10.12775/llp.2019.014

Cited by 10 publications

(14 citation statements)

References 42 publications

(99 reference statements)

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“…Indeed, in virtue of the fact that in Triadic logic non-falsity is not equivalent to truth, we can rightfully (from the traditional point of view) assert the falsity of a disjunction when one of its disjuncts is false, and another is not false. This echoes the 'infectious' interpretation of truth value gaps and their role in the epistemic status of disjunctive sentences (see [3,22,29,30] for the discussion on that topic).…”

Section: Conjunction? Disjunction?mentioning

confidence: 73%

Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

Belikov

2021

LLP

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In this paper, we present two variants of Peirce's Triadic Logic within a language containing only conjunction, disjunction, and negation. The peculiarity of our systems is that conjunction and disjunction are interpreted by means of Peirce's mysterious binary operations Ψ and Φ from his 'Logical Notebook'. We show that semantic conditions that can be extracted from the definitions of Ψ and Φ agree (in some sense) with the traditional view on the semantic conditions of conjunction and disjunction. Thus, we support the conjecture that Peirce's special interest in these operations is due to the fact that he interpreted them as conjunction and disjunction, respectively. We also show that one of our systems may serve as a suitable base for an interesting implicative expansion, namely the connexive threevalued logic by Cooper. Sound and complete natural deduction calculi are presented for all systems examined in this paper.

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Section: Conjunction? Disjunction?mentioning

confidence: 73%

Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

Belikov

2021

LLP

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“…One of these concerns the potential to generalize the techniques implemented to work with PAI fde , in order to characterize different relevant logics complying with principles other than Parry's. In this vein, one may look at what is called the dual of Parry's Proscriptive Principle in, e.g., [12] and [45], which requires that for a first-degree entailment of the form ϕ → ψ, it holds that V ar(ϕ) ⊆ V ar(ψ).…”

Section: Resultsmentioning

confidence: 99%

“…Our first goal is to develop a simple matrix semantics for PAI fde , following the standard techniques of Abstract Algebraic Logic discussed, e.g., in [23]. Our second goal is to develop a simple sequent calculus for PAI fde , following the techniques applied to obtain linguistically constrained sequent calculi presented, e.g., in [11], [12], [14], [24], and [45].…”

Section: Background and Aimmentioning

confidence: 99%

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A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication

Szmuc

2021

Stud Logica

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We provide a logical matrix semantics and a Gentzen-style sequent calculus for the first-degree entailments valid in W. T. Parry's logic of Analytic Implication. We achieve the former by introducing a logical matrix closely related to that inducing paracomplete weak Kleene logic, and the latter by presenting a calculus where the initial sequents and the left and right rules for negation are subject to linguistic constraints. 1 The main publications which featured presentations of this system were his Doctoral Thesis [34], and his articles [35], [36], [37], [38], and the posthumously published [39]. 2 These paradoxes pertain to the fact that, on the one hand, necessarily true propositions (e.g., logical truths) are implied by any proposition whatsoever and, on the other hand, necessarily false propositions (e.g., logical contradictions) imply any proposition whatsoever.

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“…As mentioned above, I proposed such a thing in [10], and that will be employed here, preceded by some discussion to motivate it. I note that this generalization has been further considered in [7], with a dualized version explored in [22,23]. We will actually make use of this dualized version, as well as of the original version.…”

Section: Introductionmentioning

confidence: 99%

Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics

Fitting

2021

AJL

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This paper continues my work of [9], which showed there was a broad family of many valued logics that have a strict/tolerant counterpart. Here we consider a generalization of weak Kleene three valued logic, instead of the strong version that was background for that earlier work. We explain the intuition behind that generalization, then determine a subclass of strict/tolerant structures in which a generalization of weak Kleene logic produces the same results that the strong Kleene generalization did. This paper provides much background, but is not self-contained. Some results from [9] are called on, and are not reproved here. [9] Melvin C. Fitting. “A Family of Strict/Tolerant Logics”. In: Journal of Philosophical Logic (2020). Online. Print publication forthcoming.

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An Epistemic Interpretation of Paraconsistent Weak Kleene Logic

Cited by 10 publications

References 42 publications

Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

Peirce’s Triadic Logic and Its (Overlooked) Connexive Expansion

A Simple Logical Matrix and Sequent Calculus for Parry’s Logic of Analytic Implication

Strict/Tolerant Logics Built Using Generalized Weak Kleene Logics

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