Constructive Negations and Paraconsistency

Odintsov, Sergei P.

doi:10.1007/978-1-4020-6867-6

Cited by 123 publications

(92 citation statements)

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“…The difference between N and N − is that explosion does not hold in the latter, but holds in the former. Following Odintsov [2003Odintsov [ , 2008, the propositional fragments of Nelson's logics N and N − have been dubbed, respectively, as N3 and N4, and the latter became the standard presentation of Nelson's paraconsistent logic. The notion of realizability [Kleene, 1945] can be understood as the formal side of the BHK interpretation of intuitionistic logic.…”

Section: A Remark On the Problem Of 'Just True Just False'mentioning

confidence: 99%

An epistemic approach to paraconsistency: a logic of evidence and truth

Carnielli

Rodrigues

2017

Synthese

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The purpose of this paper is to present a paraconsistent formal system and a corresponding intended interpretation according to which true contradictions are not tolerated. Contradictions are, instead, epistemically understood as conflicting evidence, where evidence for a proposition A is understood as reasons for believing that A is true. The paper defines a paraconsistent and paracomplete natural deduction system, called the Basic Logic of Evidence (BLE ), and extends it to the Logic of Evidence and Truth (LETJ ). The latter is a logic of formal inconsistency and undeterminedness that is able to express not only preservation of evidence but also preservation of truth. LETJ is anti-dialetheist in the sense that, according to the intuitive interpretation proposed here, its consequence relation is trivial in the presence of any true contradiction. Adequate semantics and a decision method are presented for both BLE and LETJ , as well as some technical results that fit the intended interpretation.

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Section: A Remark On the Problem Of 'Just True Just False'mentioning

confidence: 99%

An epistemic approach to paraconsistency: a logic of evidence and truth

Carnielli

Rodrigues

2017

Synthese

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“…Then one of the topics that might be interesting is to see the connection between logics with two negations such as systems of Nelson (cf. [13,20]) and connexive logic (cf. [28]).…”

Section: Resultsmentioning

confidence: 99%

Negative Modalities in the Light of Paraconsistency

Omori

Waragai

2015

Studies in Universal Logic

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Modality and non-classical negation have some interesting connections. One of the most famous connections is the relation between S4-modality and intuitionistic negation. In this chapter, we focus on the negative modalities in the perspective of paraconsistency. The basic idea here is to consider the negative modality defined as 'not necessarily' or equivalently 'possibly not' where 'not' is classical negation, and 'necessarily' and 'possibly' are modalities in modal logics. This chapter offers a solution to the problem of axiomatizing systems of modal logic such as D and S4 in terms of negative modalities. One of the upshots of this solution is that we may consider the semantics of paraconsistency with the help of various considerations known in the literature of modal logics related to D and S4.

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“…The rest of this section closely follows the presentation of the system N4 offered by Odintsov in [19], including his adaptation, for N4, of the semantics proposed by Fidel in [20] for Nelson's system N , as well as the semantics in terms of twist structures. A variant of twist structures for LFIs will be introduced in Chap.…”

Section: Nelson's Paraconsistent Logic N4mentioning

confidence: 98%

“…to N4, the system N4 ⊥ is obtained, which is defined over the signature 2 = {⊥, ∧, ∨, →, ¬}, being a conservative extension of N4 (see [19]). The intuitionistic negation ∼ can be defined in N and N4 ⊥ as ∼α…”

Section: Nelson's Paraconsistent Logic N4mentioning

confidence: 99%

LFIs Based on Other Logics

Carnielli

Coniglio

2016

Paraconsistent Logic: Consistency, Contradiction and Negation

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In the previous chapters, all the LFIs studied were based on positive classical logic, CPL + . The basic system considered was mbC, and several extensions of it were proposed. Moreover, we have arrived at several 3-valued logics, most of them algebraizable in the sense of Blok and Pigozzi.In this chapter, we will analyze LFIs defined over other logical bases: positive intuitionistic logic, the four-valued Belnap's logic and some families of fuzzy logics, as well as positive modal logics.

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Constructive Negations and Paraconsistency

Cited by 123 publications

References 0 publications

An epistemic approach to paraconsistency: a logic of evidence and truth

An epistemic approach to paraconsistency: a logic of evidence and truth

Negative Modalities in the Light of Paraconsistency

LFIs Based on Other Logics

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