Generalized correspondence analysis for three-valued logics
type: Item
instance of: scholarly article
title: Generalized correspondence analysis for three-valued logics
zbMATH Open document ID: 1435.03047
published in: Logica Universalis
publication date: 2018-12-12T00:00:00Z
review text: This paper extends the correspondence analysis of \textit{B. Kooi} and \textit{A. Tamminga} [Rev. Symb. Log. 5, No. 4, 720--730 (2012; Zbl 1270.03045)] to a larger class of three-valued logics. It generalizes the results from the author and \textit{V. Shangin} [Rev. Symb. Log. 10, No. 4, 756--781 (2017; Zbl 1387.03009)], and from the author [Log. Log. Philos. 26, No. 2, 197--206 (2017; Zbl 1417.03181); Log. Univers. 11, No. 4, 525--532 (2017; Zbl 1385.03032); Log. Log. Philos. 27, No. 1, 53--66 (2018; Zbl 1456.03048); Mosc. Univ. Math. Bull. 73, No. 1, 30--33 (2018; Zbl 1390.03024); Mosc. Univ. Math. Bull. 72, No. 3, 133--136 (2017; Zbl 1396.03048)] regarding deduction systems for three-valued logics. It is shown that the method of correspondence analysis works for the negative fragments of the paraconsistent logic of paradox $\mathbf{LP}$ and the strong Kleene logic $\mathbf{K_3}$ and that this method is also suitable for the negative fragments of Heytings's logic $\mathbf{G_3}$ and its dual $\mathbf{DG_3}$. The power of generalized correspondence analysis is illustrated with examples of $\mathbf{LP}$ and the logics $\mathbf{L3A}$ and $\mathbf{L3B}$ of \textit{J.-Y. Beziau} and \textit{A. Franceschetto} [Springer Proc. Math. Stat. 152, 131--145 (2015; Zbl 1423.03097)].
reviewed by: Albert Hoogewijs
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B22
Mathematics Subject Classification ID: 03F03
Mathematics Subject Classification ID: 03B53
zbMATH DE Number: 6992801
zbMATH Keywords: proof theory
zbMATH Keywords: paraconsistent logic
zbMATH Keywords: correspondence analysis
zbMATH Keywords: natural deduction
zbMATH Keywords: paracomplete logic
zbMATH Keywords: three-valued logic
author: Yaroslav I. Petrukhin
MaRDI profile type: Publication
full work available at URL: s11787-018-0212-9
OpenAlex ID: W2895942613
cites work: Q4085699
cites work: A calculus of antinomics
cites work: Logic of antinomies
cites work: On an implication connective of RM
cites work: Natural 3-valued logics—characterization and proof theory
cites work: Q3909031
cites work: Q4487295
cites work: Two Genuine 3-Valued Paraconsistent Logics
cites work: New directions in paraconsistent logic. Collected papers of the 5th world congress on paraconsistency, WCP, Kolkata, India, February 13--17, 2014
cites work: On a three-valued logical calculus and its application to the analysis of the paradoxes of the classical extended functional calculus
cites work: On paraconsistent weak Kleene logic: axiomatisation and algebraic analysis
cites work: The first law of cubology for the Rubik’s Revenge
cites work: Q4982108
cites work: Anti-intuitionism and paraconsistency
cites work: Q4639914
cites work: Formal inconsistency and evolutionary databases
cites work: Logics of Formal Inconsistency
cites work: Paraconsistency and Sette’s calculus P1
cites work: A weakly-intuitionistic logic \(I1\)
cites work: Q4992398
cites work: A map of dependencies among three-valued logics
cites work: On the theory of inconsistent formal systems
cites work: Неклассические модификации многозначных матриц классической логики. Часть I.
cites work: Q5596218
cites work: Über Eine Prädikatenlogik mit Partiell Definierten Prädikaten und Funktionen
cites work: Logics of nonsense and Parry systems
cites work: Nonsense logics and their algebraic properties
cites work: Q4296301
cites work: A note on matrices for systems of nonsense-logics
cites work: Q5800353
cites work: The pursuit of an implication for the logics L3A and L3B
cites work: A propositional calculus for inconsistent deductive systems
cites work: Bochvar's three-valued logic and literal paralogics: Their lattice and functional equivalence
cites work: Q3567765
cites work: Rational agency from a truth-functional perspective
cites work: COMPLETENESS VIA CORRESPONDENCE FOR EXTENSIONS OF THE LOGIC OF PARADOX
cites work: Literal-paraconsistent and literal-paracomplete matrices
cites work: Q5613169
cites work: Q3606211
cites work: Q4229041
cites work: Q5551428
cites work: Q3705494
cites work: Brief study of G'3 logic
cites work: AUTOMATED CORRESPONDENCE ANALYSIS FOR THE BINARY EXTENSIONS OF THE LOGIC OF PARADOX
cites work: Q5240589
cites work: Q2981255
cites work: Q4997950
cites work: Natural deduction for three-valued regular logics
cites work: Natural deduction for Fitting's four-valued generalizations of Kleene's logics
cites work: Natural Deduction for Four-Valued both Regular and Monotonic Logics
cites work: Natural deduction for Post's logics and their duals
cites work: The natural deduction systems for the three-valued nonsense logics Z and E
cites work: Natural deduction system for three-valued Heyting's logic
cites work: Q4440793
cites work: The logic of paradox
cites work: Q5661846
cites work: A Routley-Meyer semantics for Gödel 3-valued logic and its paraconsistent counterpart

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cites work: On interpretation of inconsistent theories

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cites work: Maximal weakly-intuitionistic logics

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cites work: Q4777260

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cites work: A Precise Definition of an Inference (by the Example of Natural Deduction Systems for Logics $I_{\langle \alpha,\beta \rangle}$

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cites work: Some remarks on three-valued logic of J. Lukasiewicz

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cites work: Q5816696

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cites work: Defining LFIs and LFUs in extensions of infectious logics

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cites work: Conjunction and disjunction in infectious logics

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cites work: Q4982110

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cites work: A Lattice of Implicative Extensions of Regular Kleene's Logics

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cites work: Q3108641

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cites work: The defective conditional in mathematics

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cites work: Stone algebras, conditional events, and three valued logic

Generalized correspondence analysis for three-valued logics (Wikidata QID)
Wikidata QID: Q129108411

Generalized correspondence analysis for three-valued logics (DOI)
DOI: 10.1007/S11787-018-0212-9