Correspondence analysis and automated proof-searching for first degree entailment

Petrukhin, Yaroslav; Shangin, Vasilyi

doi:10.1007/s40879-019-00344-5

Cited by 14 publications

(12 citation statements)

References 65 publications

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“…Yet another way to obtain a natural deduction system for a many-valued logic is to present a sequent calculus for this logic, following Avron's [3] approach (see also a later paper by Avron, Ben-Naim, and Konikowska [4]) and transform this sequent calculus to the natural deduction system. A comparison of correspondence analysis and Avron, Ben-Naim, and Konikowska's method one may find in [26].…”

Section: Natural Deduction For Liramentioning

confidence: 99%

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The Logic of Internal Rational Agent

Petrukhin

2021

AJL

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In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent \textbf{LRA} \cite{LRA}. We call our logic $ \bf LIRA$ (Logic of Internal Rational Agency). In contrast to \textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic \cite{ZS}. This logic may be useful in a situation when according to an agent's point of view (i.e. internal point of view) her/his reasoning is rational, while from the external one it might be not the case. One may use \textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for \textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations (as well as their combination) of \textbf{LRA}, two more possibility operators for \textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $\bf LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $\bf LIRA$ (including $\bf LIRA$ itself) as well as their basic modal extension via linear-type natural deduction systems.

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Section: Natural Deduction For Liramentioning

confidence: 99%

“…, k . In contrast to [18,39,28,26], we present all the rules in a general way, i.e. we introduce one equivalence from which all the rules for all the equations of the form (x 1 , .…”

Section: Natural Deduction For Liramentioning

confidence: 99%

The Logic of Internal Rational Agent

Petrukhin

2021

AJL

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“…Further, Petrukhin [23] formulated via correspondence analysis natural deduction systems for all the unary and binary extensions of Belnap-Dunn's four-valued logic FDE (First Degree Entailment) [2,3,7] supplied with Boolean negation. 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.…”

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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“…It has to be mentioned that Petrukhin and Shangin defined natural deduction systems for binary extensions of FDE from the point of view of correspondence analysis in a recent paper[16]. More specifically, in Section 2 of that paper they refer to the eight matrices discussed in the conclusions of[18], which are the same ones employed to develop the Lti-logics in the present paper.…”

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confidence: 98%

Belnap-Dunn Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer’s Logic B

López

2021

LLP

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The logics BN4 and E4 can be considered as the 4-valued logics of the relevant conditional and (relevant) entailment, respectively. The logic BN4 was developed by Brady in 1982 and the logic E4 by Robles and Méndez in 2016. The aim of this paper is to investigate the implicative variants (of both systems) which contain Routley and Meyer's logic B and endow them with a Belnap-Dunn type bivalent semantics.

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Correspondence analysis and automated proof-searching for first degree entailment

Cited by 14 publications

References 65 publications

The Logic of Internal Rational Agent

The Logic of Internal Rational Agent

The Method of Socratic Proofs Meets Correspondence Analysis

Belnap-Dunn Semantics for the Variants of BN4 and E4 which Contain Routley and Meyer’s Logic B

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