Generalized Correspondence Analysis for Three-Valued Logics

Petrukhin, Yaroslav

doi:10.1007/s11787-018-0212-9

Cited by 14 publications

(8 citation statements)

References 49 publications

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“…, • n . In [28], it was shown that for the same logics (and some others) it is enough to consider the {¬}-language for the basic system. In [27], basic systems were built in the {¬, ∼, ∧, ∨}-language.…”

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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“…Petrukhin [24] presented via correspondence analysis natural deduction systems for all the unary and binary extensions of Kubyshkina and Zaitsev's [18] four-valued logic LRA (Logic of Rational Agent). Besides, he generalized Kooi and Tamminga's ( [15], [33]) results for a wider class of three-valued logics [25]. Petrukhin and Shangin [30] used correspondence analysis to syntactically characterize Tomova's natural logics [34,12].…”

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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“…Consider, e.g., the rule B ∧ ¬B ⊢ ((A ⊃ B) ∧ ¬(A ⊃ B)) ∨ ¬A. Better rules may be found in (Petrukhin, 2018), where generalised correspondence analysis is presented, but such a system has eleven rules for implication. We present one with four rules for implication and show that it is normalisable.…”

Section: Introduction: Motivation and Related Workmentioning

confidence: 99%

“…A natural deduction system for K 3 which we are going to consider is a modification of Priest's system (Priest, 2002). 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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Generalized Correspondence Analysis for Three-Valued Logics

Cited by 14 publications

References 49 publications

The Logic of Internal Rational Agent

The Logic of Internal Rational Agent

The Method of Socratic Proofs Meets Correspondence Analysis

Normalisation for Some Quite Interesting Many-Valued Logics

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