Paraconsistent logics and paraconsistency (original) (raw)

Paraconsistency: Logic and Applications - Springer

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

Paraconsistent Logic: A Proof-Theoretical Approach*

2006

A logic is paraconsistent if it allows for non-trivial inconsistent theories. Given the usual definition of inconsistency, the notion of paraconsistent logic seems to rely upon the interpretation of the sign ‘¬’. As paraconsistent logic challenges properties of negation taken to be basic in other contexts, it is disputable that an operator lacking those properties will count as real negation. The conclusion is that there cannot be truly paraconsistent logics. This objection can be met from a substructural perspective since paraconsistent sequent calculi can be built with the same operational rules as classical logic but with slightly different structural rules.

Remarks on the applications of paraconsistent logic to physics

2003

In this paper we make some general remarks on the use of non-classical logics, in particular paraconsistent logic, in the foundational analysis of physical theories. As a case-study, we present a reconstruction of P.\-D.\ F\'evrier's' logic of complementarity'as a strict three-valued logic and also a paraconsistent version of it. At the end, we sketch our own approach to complementarity, which is based on a paraconsistent logic termed'paraclassical logic'.

Three decades of paraconsistent annotated logics: a review paper on some applications

Procedia Computer Science, 2019

In this expository work, we sketch some applications of annotated logics. Such logics were discovered in the late 1980s and nowadays have become one of the most fertile logics for applications. They constitute a two-sorted logic, and they are paraconsistent and in general paracomplete and non-alethic logics.

What is a Paraconsistent Logic

Paraconsistent logics are logical systems that reject the classical conception, usually dubbed Explosion, that a contradiction implies everything. However, the received view about paraconsistency focuses only the inferential version of Explosion, which is concerned with formulae, thereby overlooking other possible accounts. In this paper, we propose to focus, additionally, on a meta-inferential version of Explosion, i.e. which is concerned with inferences or sequents. In doing so, we will offer a new characterization of paraconsistency by means of which a logic is paraconsistent if it invalidates either the inferential or the meta-inferential notion of Explosion. We show the non-triviality of this criterion by discussing a number of logics. On the one hand, logics which validate an invalidate both versions of Explosion, such as classical logic and Asenjo-Priest's 3-valued logic LP. On the other hand, logics which validate one version of Explosion but not the other, such as the substructural logics TS and ST, introduced by Malinowski and Cobreros, Egré, Ripley and van Rooij, which are obtained via Malinowski's and Frankowski's q-and p-matrices, respectively.

A knowledge representation perspective: Logics for paraconsistent reasoning

International Journal of Intelligent Systems, 1994

Paraconsistent logics are examined as an approach to knowledge representation devoted to the formalization of reasoning in the presence of contradictions. The adequacy of paraconsistent logics in such a perspective is described both on a general level and on a more specific level: discussion involves representative examples as well as special features (in the form of logical principles) of some significant paraconsistent logics. There is also a comparison of the paraconsistent logics approach with two alternative approaches, namely belief revision and non-monotonic logics.

The inapplicability of (selected) paraconsistent logics

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained in that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalize to a large class of paraconsistent logics. A wide class of paraconsistent (inconsistency-tolerant) logics is obtained by filtration: adding conditions on the classical consequence operation (one example is weak Rescher-Manor consequence --- which bears Gamma\GammaGamma to phi\phiphi just in case phi\phiphi follows classicaly from at least one maximally consistent subset of Gamma\GammaGamma). We start with surveying the most promising candidates and comparing their strength. Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to chose any of the filtered logics for action-guiding reasoning with inconsistent information, roughly because such a reasoning has to start with selecting possible scenarios and such a process does not correspond to any of the mathematical models offered by filtered paraconsistent logics. Finally, we criticize a recent attempt to defend explorative hypothetical reasoning by means of weak Rescher-Manor consequence operation by Meheus et al.

An Overview of Paraconsistent Logic in the 8Os

Journal of Non-Classical Logic 6, 5-32, 1989

In this paper we aim at giving a sketch ofsotne aspects ofthe state of development of paraconsistent logic in the 80s. Our exposition will not aim at completeness. Given the developrnent of the literature in the field, completeness is out of question in a paper like ours.