Ideal Paraconsistent Logics

Arieli, Ofer; Avron, Arnon; Zamansky, Anna

doi:10.1007/s11225-011-9346-y

Cited by 49 publications

(55 citation statements)

References 26 publications

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“…D'Ottaviano in [12]. Therefore, their study is also interesting in order to obtain new paraconsistent logics from Lukasiewicz logics and, perhaps, like in the case of L(F 1/3 ), some ideal paraconsistent logic in the sense of [2].…”

Section: Discussionmentioning

confidence: 99%

On the set of intermediate logics between the truth- and degree-preserving Łukasiewicz logics

2016

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The aim of this paper is to explore the class of intermediate logics between the truth-preserving Lukasiewicz logic L and its degree-preserving companion L ≤ . From a syntactical point of view, we introduce some families of inference rules (that generalize the explosion rule) that are admissible in L ≤ and derivable in L and we characterize the corresponding intermediate logics. From a semantical point of view, we first consider the family of logics characterized by matrices defined by lattice filters in [0, 1], but we show there are intermediate logics falling outside this family. Finally, we study the case of finite-valued Lukasiewicz logics where we axiomatize a large family of intermediate logics defined by families of matrices (A, F ) such that A is a finite MV-algebra and F is a lattice filter.

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Section: Discussionmentioning

confidence: 99%

On the set of intermediate logics between the truth- and degree-preserving Łukasiewicz logics

2016

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“…Of two intellectual acts, to assert a proposition and to reject it, 3 only the first has been taken into account in modern formal logic. Gottlob Frege introduced into logic the idea of assertion, and the sign of assertion (⊢), accepted afterwards by the authors of Principia Mathematica.…”

Section: Refutationmentioning

confidence: 99%

A Generalisation of a Refutation-related Method in Paraconsistent Logics

Trybus

2018

LLP

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Abstract. This article describes a refutation method of proving the maximality of three-valued paraconsistent logics. After outlining the philosophical background related to paraconsistent logics and the refutation approach to modern logic, we briefly describe how these two areas meet in the case of maximal paraconsistent logics. We focus on a method of proving maximality introduced in [34] and [37] that has the benefit of being simple and effective. We show how the method works on a number of examples, thus emphasising the fact that it provides a unifying approach to the search for maximal paraconsistent logics. Finally, we show how the method can be generalised to cover a wide range of paraconsistent logics. We also conduct a small experiment that confirms the theoretical results.

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“…The common idea behind these approaches is that the negative information (reasons, values) is not just the complement of the positive one, but needs to be considered explicitly and formalised appropriately. In formal logic this idea has been further developing multi-valued logics and more precisely four-valued logics (see in [17], [18], [32], [100], [109], [106], [121], [155], [248], [253]). In the case of preference modelling, the use of such logics was first suggested in [252] and [82].…”

Section: Beyond Fuzzy Setsmentioning

confidence: 99%