Exploring Paraconsistency in Degree-Preserving Fuzzy Logics

Ertola, Rodolfo; Esteva, Francesc; Flaminio, Tommaso; Godo, Lluı́s; Noguera, Carles

doi:10.2991/eusflat.2013.17

Cited by 3 publications

(10 citation statements)

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“…2. While FT is boldly paraconsistent (see Corollary 6.2 above), all paraconsistent degree-preserving fuzzy logics are partially ¬-explosive (see Note 6.3) with respect to ¬q ∨ q (Proposition 8 of [7]). 3.…”

Section: Ft As a Semi-relevant Logicmentioning

confidence: 95%

“…Hence FT is strongly paraconsistent. logic Ł ∞ (but not Gödel logic), L ≤ is a paraconsistent logic (see [7] for more details). In what follows we list what we believe to be the main differences (and similarities) between FT and the paraconsistent degree-preserving fuzzy logics (especially Ł ≤ ∞ , the degree-preserving fuzzy logic derived from Łukasiewicz logic Ł ∞ ).…”

Section: Ft As a Semi-relevant Logicmentioning

confidence: 99%

“…An alternative method of constructing paraconsistent fuzzy logics have been suggested and explored in [7]. The idea is to turn a given (standard) fuzzy logic L into a paraconsistent logic L ≤ by letting T L ≤ ψ iff there exists a finite {ϕ 1 , .…”

Section: Proposition 64 Anderson and Belnap's System E Is Included mentioning

confidence: 99%

“…The notion of strong consistency, in turn, has a crucial role in [2]. Now in the terminology of [4] (again repeated in [7]), strong paraconsistency of a logic L means that L is not partially ¬-explosive with respect to ¬q, while bold paraconsistency of L means that L is not partially ¬-explosive with respect to any formula. Hence bold paraconsistency implies strong paraconsistency.…”

mentioning

confidence: 99%

“…With the exception of strong consistency, the exact definitions of the various notions mentioned in Corollary 6.2 are given in [4] (and repeated in [7]). It is straightforward to see that according to those official definitions, the properties of FT that we mention in the first parts of the various items of Corollary 6.2 indeed immediately imply the "Hence" parts of those items.…”

mentioning

confidence: 99%

See 4 more Smart Citations

Paraconsistent fuzzy logic preserving non-falsity

Avron

2016

Fuzzy Sets and Systems

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Section: Ft As a Semi-relevant Logicmentioning

confidence: 95%

Section: Ft As a Semi-relevant Logicmentioning

confidence: 99%

Section: Proposition 64 Anderson and Belnap's System E Is Included mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Paraconsistent fuzzy logic preserving non-falsity

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Logics of Formal Inconsistency Enriched With Replacement: An Algebraic and Modal Account

Carnielli

Coniglio

Fuenmayor³

2021

The Review of Symbolic Logic

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One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold for several systems of the hierarchy of paraconsistent logics known as Logics of Formal Inconsistency (LFIs). Because of this, these logics are uniquely characterized by semantics of non-deterministic kind. This paper offers a solution for two open problems in the domain of paraconsistency, in particular connected to algebraization of LFIs, by obtaining several LFIs weaker than C 1 , each of one is algebraizable in the standard Lindenbaum-Tarski's sense by a suitable variety of Boolean algebras extended with operators. This means that such LFIs satisfy the replacement property. The weakest LFI satisfying replacement presented here is called RmbC, which is obtained from the basic LFI called mbC. Some axiomatic extensions of RmbC are also studied, and in addition a neighborhood semantics is defined for such systems. It is shown that RmbC can be defined within the minimal bimodal non-normal logic E ⊕ E defined by the fusion of the non-normal modal logic E with itself. Finally, the framework is extended to first-order languages. RQmbC, the quantified extension of RmbC, is shown to be sound and complete w.r.t. BALFI semantics.

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Logics of formal inconsistency arising from systems of fuzzy logic

Coniglio¹,

Esteva²,

Godo³

2014

Logic Journal of IGPL

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This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and inconsistency in the style of the so-called Logics of Formal Inconsistency (LFIs). The main novelty of the present approach is the definition of postulates for this type of operators over MTL-algebras, leading to the definition and axiomatization of a family of logics, expansions of MTL, whose degree-preserving counterpart are paraconsistent and moreover LFIs.

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Exploring Paraconsistency in Degree-Preserving Fuzzy Logics

Cited by 3 publications

References 17 publications

Paraconsistent fuzzy logic preserving non-falsity

Paraconsistent fuzzy logic preserving non-falsity

Logics of Formal Inconsistency Enriched With Replacement: An Algebraic and Modal Account

Logics of formal inconsistency arising from systems of fuzzy logic

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