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Paraconsistent logic

About: Paraconsistent logic is a research topic. Over the lifetime, 1610 publications have been published within this topic receiving 28842 citations.


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Journal ArticleDOI
Ken Akiba1
01 Oct 1999-Mind
TL;DR: In this paper, the authors argue that the notion of possible truth in subvaluationism can be interpreted as a kind of necessary truth in a certain sense of "possible".
Abstract: Dominic Hyde (1997) has presented a new logical system for vague words that employs paraconsistent logic. He called it subvaluationism, in analogy with supervaluationism Fine (1975) and others have made popular. Hyde maintained that subvaluationism is substantially different from supervaluationism, and is at least as good for a logic of vagueness. In this note, I shall argue for the following: First, we may reasonably take Hyde's so-called subtruth not as truth simpliciter, as Hyde does, but just as possible truth in a certain sense of "possible". Second, we also may take supertruth in supervaluationism as the dual of subtruth, a kind of necessary truth; we do not have to take it as truth simpliciter, either. We can regard superand subvaluationism essentially as duals. Finally, if we interpret superand subtruth this way, we can make inference rules for vague words much simpler and in compliance with classical logic. The logic of superand subvaluationism can be regarded not as an alternative to classical logic but as an extension of it. We do not need non-classical logic to understand vagueness. Superand subvaluationism make use of the notion of (admissible) precisification. An admissible precisification of a vague predicate (or singular term) is an admissible interpretation under which a particular precise extension (or denotation) is assigned to the word. Even a vague sentence is either true or false on an admissible precisification. (In what follows I shall drop the adjective "admissible" for the sake of simplicity and just say "precisification" when I mean "admissible precisification". What is admissible and what not has been a matter of controversy, but I set aside that problem.) According to supervaluationism, a sentence is supertrue if and only if it is true on all precisifications, superfalse if and only if it is false on all precisifications, and neither supertrue nor superfalse if and only if it is true on some precisifications and false on the others. According to subvaluationism, a sentence is subtrue if and only if it is true on some precisifications, and subfalse if and only if it is false on some precisifications. If a sentence is true on some precisifications and false on the others, it is considered both subtrue and subfalse. In both theories, all logical truths are superor subtrue because they are true on all (thus, some)

6 citations

Book ChapterDOI
01 Jan 2017
TL;DR: In this paper, the authors examine up to which point Modern logic can be qualified as non-Aristotelian and compare it with propositional and first-order logic.
Abstract: In this paper we examine up to which point Modern logic can be qualified as non-Aristotelian. After clarifying the difference between logic as reasoning and logic as a theory of reasoning, we compare syllogistic with propositional and first-order logic. We touch the question of formal validity, variable and mathematization and we point out that Gentzen’s cut-elimination theorem can be seen as the rejection of the central mechanism of syllogistic – the cut-rule having been first conceived as a modus Barbara by Hertz. We then examine the non-Aristotelian aspect of some non-classical logics, in particular paraconsistent logic. We argue that a paraconsistent negation can be seen as neo-Aristotelian since it corresponds to the notion of subcontrary in Boethius’ square of opposition. We end by examining if the comparison promoted by Vasiliev between non-Aristotelian logic and non-Euclidian geometry makes sense.

6 citations

Journal ArticleDOI
TL;DR: A new paraconsistent logic (daC'), which is weaker than logic $${{\mathbb{Z}}}$$Z and G′3, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism.
Abstract: By weakening an inference rule satisfied by logic daC, we define a new paraconsistent logic (daC '), which is weaker than logic $${{\mathbb{Z}}}$$ and G′ 3, enjoys properties presented in daC like the substitution theorem, and possesses a strong negation which makes it suitable to express intutionism. Besides, daC ' helps to understand the relationships among other logics, in particular daC, $${{\mathbb{Z}}}$$ and PH1.

6 citations

Journal ArticleDOI
TL;DR: In this paper, the negation of a proposition is defined by a fixed proposition and a number of standard properties of negation, including reductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic.
Abstract: In positive logic the negation of a propositionA is defined byA ⊃X whereX is some fixed proposition. A number of standard properties of negation, includingreductio ad absurdum, can then be proved, but not the law of noncontradiction so that this forms a paraconsistent logic. Various stronger paraconsistent logics are then generated by putting in particular propositions forX. These propositions range from true through contingent to false.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202313
202255
202131
202036
201935
201847