Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox

Petrukhin, Yaroslav; Shangin, Vasilyi

doi:10.1017/s1755020317000156

Cited by 10 publications

(6 citation statements)

References 27 publications

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“…In particular, Kooi and Tamminga [21] study truth-functional extensions of LP (cf. [24] and [25]) in a natural deduction setting, whereas Petrukhin and Shangin [23] investigate some implicational extensions of LP, including extensions by natural implications in the sense of Tomova [34]. Also, Thomas [33] has to be mentioned.…”

Section: Definition 81 (T -Interpretations)mentioning

confidence: 99%

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

Robles

Méndez

2019

Journal of Applied Non-Classical Logics

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A conditional is natural if it fulfills the three following conditions. (1) It coincides with the classical conditional when restricted to the classical values  and  ; (2) it satisfies the Modus Ponens; and (3) it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a "bivalent" Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two designated elements. (We understand the notion "natural conditional" according to N. Tomova, "A lattice of implicative extensions of regular Kleene's logics",

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Section: Definition 81 (T -Interpretations)mentioning

confidence: 99%

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

Robles

Méndez

2019

Journal of Applied Non-Classical Logics

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“…Petrukhin and Shangin have recently applied correspondence analysis and a proof-searching procedure for FDE itself [29]. Petrukhin and Shangin [26] developed a proof-searching algorithm for natural deduction systems for all the binary extensions of LP. In [27], the authors extended their proof searching technique to the case of all the binary extensions of K 3 .…”

Section: The Notion Of Correspondence Analysismentioning

confidence: 99%

The Method of Socratic Proofs Meets Correspondence Analysis

2019

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The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic (i.e. pertaining to the logic of questions) calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. In this paper it is used to consider sequent calculi with non-branching (the only exception being the rule of cut), invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions.

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“…One may find natural deduction systems (with a huge amount of rules) for any unary/binary tabular extensions of K 3 in (Tamminga, 2014) and (Petrukhin, 2018). A systematic treatment of linear-type natural deduction systems and automatic proof search for (unary and binary) truthtabular extensions of LP, K 3 and FDE may be found in (Petrukhin and Shangin, 2017, 2020.…”

Section: Introduction: Motivation and Related Workmentioning

confidence: 99%

Normalisation for Some Quite Interesting Many-Valued Logics

Kürbis

Petrukhin

2021

LLP

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In this paper, we consider a set of quite interesting three-and four-valued logics and prove the normalisation theorem for their natural deduction formulations. Among the logics in question are the Logic of Paradox, First Degree Entailment, Strong Kleene logic, and some of their implicative extensions, including RM3 and RM ⊃ 3 . Also, we present a detailed version of Prawitz's proof of Nelson's logic N4 and its extension by intuitionist negation.

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Automated Correspondence Analysis for the Binary Extensions of the Logic of Paradox

Cited by 10 publications

References 27 publications

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values

The Method of Socratic Proofs Meets Correspondence Analysis

Normalisation for Some Quite Interesting Many-Valued Logics

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