Paraconsistent Logic

Priest, Graham

doi:10.1007/978-94-017-0460-1_4

Cited by 337 publications

(152 citation statements)

References 66 publications

Supporting

Mentioning

146

Contrasting

Unclassified

Order By: Relevance

“…In brief, paraconsistency is about handling contradictions in a coherent way, and many approaches have been investigated [1,2,9,11,31,32,46]. In classical logic there are only two truth values and everything follows from a contradiction, but in a paraconsistent logic not everything follows from a contradiction.…”

Section: Paraconsistencymentioning

confidence: 99%

Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant

Villadsen

Schlichtkrull

2017

Transactions on Large-Scale Data- And Knowledge-Centered Systems XXXIV

View full text Add to dashboard Cite

Abstract. We present a formalization of a so-called paraconsistent logic that avoids the catastrophic explosiveness of inconsistency in classical logic. The paraconsistent logic has a countably infinite number of nonclassical truth values. We show how to use the proof assistant Isabelle to formally prove theorems in the logic as well as meta-theorems about the logic. In particular, we formalize a meta-theorem that allows us to reduce the infinite number of truth values to a finite number of truth values, for a given formula, and we use this result in a formalization of a small case study.

show abstract

Section: Paraconsistencymentioning

confidence: 99%

Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant

Villadsen

Schlichtkrull

2017

Transactions on Large-Scale Data- And Knowledge-Centered Systems XXXIV

View full text Add to dashboard Cite

show abstract

“…For a basic presentation of this logical theory, see Priest (2004), also Horn (2006, section 4). On paraconsistent logic in general, see Priest and Tanaka (2007).) 20 It is worth noting that it is only a total denial of the LNC (i.e., the claim that all contradictory predicates equally apply and do not apply) that seems to lead to a breakdown of meaningful language.…”

Section: The Pyrrhonist's Non-dogmatic Observance Of the Lncmentioning

confidence: 99%

Pyrrhonism and the Law of Non-Contradiction

Machuca

2011

Pyrrhonism in Ancient, Modern, and Contemporary Philosophy

View full text Add to dashboard Cite

The question of whether the Pyrrhonist 1 adheres to certain logical principles, criteria of justification, and inference rules is of central importance for the study of Pyrrhonism. Its significance lies in that, whereas the Pyrrhonist describes his philosophical stance and argues against the Dogmatists by means of what may be considered a rational discourse, adherence to any such principles, criteria, and rules does not seem compatible with the radical character of his skepticism. Hence, if the Pyrrhonist does endorse them, one must conclude that he is inconsistent in his outlook. Despite its import, the question under consideration has not received, in the vast literature on Pyrrhonism of the past three decades, all the attention it deserves. In the present paper, I do not propose to provide a full examination of the Pyrrhonist's attitude towards rationality, but to focus on the question of whether he endorses the law of non-contradiction (hereafter LNC). 2 However, I will also briefly tackle the question of the Pyrrhonist's outlook on both the canons of rational justification at work in the so-called Five Modes of Agrippa and the logical rules of inference. In addition, given that the LNC is deemed a fundamental principle of rationality, determining the Pyrrhonist's attitude towards it will allow us to understand his general attitude towards rationality.In Section 1, I briefly present and analyze the LNC by distinguishing its three most common formulations. This provides the necessary framework for examining 1 I will employ interchangeably the terms "Pyrrhonist" and "Skeptic" (with a capital "S") to refer to the philosopher whose outlook is described and defended in Sextus Empiricus' surviving writings. I will say nothing about the outlooks adopted by Pyrrho, Timon, or Aenesidemus. Also, following Sextus, I use the term "Dogmatist" (δoγματικóς) to designate anyone who makes positive or negative assertions about how things really are on the basis of what he considers to be evidence and rational arguments. 2 I should note that, when using the language of adherence, endorsement, or espousal, I refer to commitment to logical principles and epistemological criteria. By contrast, when speaking of observance, I will not necessarily presuppose any such commitment: the observance of, say, a rule may consist in simple obedience without strong adherence.

show abstract

“…But there are a lot of different paraconsistent logics (see e.g. [28,13,60]), so choosing a particular logic is already a real, non-trivial commitment. So one has to be careful for avoiding stating ad hoc properties, according to a given paraconsistent logic.…”

Section: Contradiction Measuresmentioning

confidence: 99%

Approaches to Measuring Inconsistent Information

Hunter

Konieczny

2005

Lecture Notes in Computer Science

101

View full text Add to dashboard Cite

Abstract. Measures of quantity of information have been studied extensively for more than fifty years. The seminal work on information theory is by Shannon [67]. This work, based on probability theory, can be used in a logical setting when the worlds are the possible events. This work is also the basis of Lozinskii's work [48] for defining the quantity of information of a formula (or knowledgebase) in propositional logic. But this definition is not suitable when the knowledgebase is inconsistent. In this case, it has no classical model, so we have no "event" to count. This is a shortcoming since in practical applications (e.g. databases) it often happens that the knowledgebase is not consistent. And it is definitely not true that all inconsistent knowledgebases contain the same (null) amount of information, as given by the "classical information theory". As explored for several years in the paraconsistent logic community, two inconsistent knowledgebases can lead to very different conclusions, showing that they do not convey the same information. There has been some recent interest in this issue, with some interesting proposals. Though a general approach for information theory in (possibly inconsistent) logical knowledgebases is missing. Another related measure is the measure of contradiction. It is usual in classical logic to use a binary measure of contradiction: a knowledgebase is either consistent or inconsistent. This dichotomy is obvious when the only deductive tool is classical inference, since inconsistent knowledgebases are of no use. But there are now a number of logics developed to draw non-trivial conclusions from an inconsistent knowledgebase. So this dichotomy is not sufficient to describe the amount of contradiction of a knowledgebase, one needs more finegrained measures. Some interesting proposals have been made for this. The main aim of this paper is to review the measures of information and contradiction, and to study some potential practical applications. This has significant potential in developing intelligent systems that can be tolerant to inconsistencies when reasoning with real-world knowledge. 190Anthony Hunter and Sébastien Konieczny

show abstract

Paraconsistent Logic

Cited by 337 publications

References 66 publications

Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant

Formalizing a Paraconsistent Logic in the Isabelle Proof Assistant

Pyrrhonism and the Law of Non-Contradiction

Approaches to Measuring Inconsistent Information

Contact Info

Product

Resources

About