Aspects of Paraconsistent Logic

Costa, Newton C. A. da; Béziau, Jean-Yves; Bueno, Otávio

doi:10.1093/jigpal/3.4.597

Cited by 47 publications

(42 citation statements)

References 3 publications

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“…One of the oldest and best known approaches to paraconsistency is da Costa's approach ( [24,25,28]), which seeks to allow the use of classical logic whenever it is safe to do so, but behaves completely differently when contradictions are involved. This approach has led to the introduction of the family of Logics of Formal (In)consistency (LFIs) ( [17,18]).…”

Section: Introductionmentioning

confidence: 99%

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Avron¹,

Konikowska²,

Zamansky³

2012

Journal of Logic and Computation

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In [5], a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the class of C-systems. For that family, the method produces in a modular way uniform Gentzen-type rules corresponding to a variety of axioms considered in the literature.

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Section: Introductionmentioning

confidence: 99%

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Avron¹,

Konikowska²,

Zamansky³

2012

Journal of Logic and Computation

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“…They appeared recently, as Marcos, Carnielli and others worked on developing a broad generalization of the C-systems, (cf. [43], [90]), investigated by Newton C. A. da Costa, one of the first pioneeres of paraconsistent logic in Brazil back in the 1950s.…”

Section: Logics Of Formal Inconsistencymentioning

confidence: 99%

“…Paraconsistent logics exclude the Principle of Non-Contradiction ( [43]) which states that from contradictory premises any formula can be derived, thus turning the logic trivial. The first person to discuss the possibility of violating this principle was Lukasiewicz, however he did not develop any logical system to formalize his studies.…”

Section: Introductionmentioning

confidence: 99%

Paraconsistency in hybrid logic

Costa

Martins

2016

J Logic Computation

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palavras-chaveParaconsistência, lógica híbrida, lógica quase-híbrida, bistrutura, frame de Kripke, satisfação dissociada, satisfação forte, modelo, medida de inconsistência. However, the information we collect is subject to inconsistencies, namely, the search for different information sources can lead us to pick up contradictions. Nowadays, by having so many means of dissemination available, that happens frequently.The aim of this work is to develop tools capable of dealing with contradictory information that can be described as hybrid logics' formulas. To build models, to compare inconsistency in different databases, and to see the applicability of this method in day-to-day life are the basis for the development of this dissertation.

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“…In formal terms: Remark 3.8.2 Axioms (co 1 )-(co 3 ) (where • is a derived connective and not a primitive connective) were proposed by Béziau in [17] for C 1 : specifically, he proposes to substitute in C 1 the three axioms of consistency propagation for binary connectives with their stronger version. This variant of C 1 was additionally studied in [18], under the name C + 1 . The counterpart of C + 1 in signature (that is, the system obtained from mbC by adding axiom schemas (ci), (cl), (cf) and (co 1 )-(co 3 ) is called Cilo (see [1,3]).…”

Section: A Stronger Consistency Propagationmentioning

confidence: 99%

“…If Cila, which satisfies consistency propagation, also satisfies strong consistency propagation, then it contains Cilo. However, by adapting an argument in [18] for C + 1 and C 1 , the formula ¬( p 1 ∨ ¬p 2 ) → (¬ p 1 ∧ p 2 ) is a theorem in Cilo but not in Cila. This shows that Cila does not satisfy strong consistency propagation, despite satisfiying consistency propagation.…”

Section: A Stronger Consistency Propagationmentioning

confidence: 99%

Some Extensions of mbC

Carnielli

Coniglio

2016

Paraconsistent Logic: Consistency, Contradiction and Negation

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Clearly, the logic mbC is the minimal extension of CPL + having a consistency operator • and a paraconsistent negation ¬, and such that it is an LFI. In this chapter, several extensions of mbC will be proposed, taking into account different features of mbC that can be strengthened or expanded. A Wider Form of Truth-Functionality for ConsistencyBy observing the quasi-matrices presented in Sect. 2.3 of Chap. 2, it becomes clear that not every connective of mbC is truth-functional (w.r.t. valuations): the tables for ¬ and • show that non-determinism exists, to a certain extent, in the evaluation process. This aspect is not a defect of the valuations for mbC: it can be proven that mbC (and several extensions of it) are not characterizable by finite matrices, adapting J. Dugundji's argument for modal logics. This topic will be briefly analyzed in Sect. 4.2 of Chap. 4.Returning to the valuation semantics for mbC, it is clear that the truth-value of a formula α partially determines the truth-value of ¬α: if α is false then ¬α must be true, but when α is true the truth-value of ¬α cannot be determined: it can be either true or false. Similarly, the truth-values of α and ¬α partially determine the truthvalue of •α in mbC: if they are both true then •α must be false, but if one of {α, ¬α} is false and the other is true (that is, if the truth-values of α and ¬α are different), the truth-value of •α is undetermined: it can be either true or false. In [1] an extension of mbC called mCi was researched, which guarantees that the truth-values of α and ¬α are sufficient to determine the truth-value of •α. However, this extension also 1 In general, names of logic systems are acronyms for the names of the axioms involved.

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Aspects of Paraconsistent Logic

Cited by 47 publications

References 3 publications

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Paraconsistency in hybrid logic

Some Extensions of mbC

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