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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
TL;DR: In this article, the authors take a closer look at the formalization of natural reasoning, inconsistency-tolerant logic, and formal analysis of causal nexus in Polish logic, taking into account the use of methods and results of formal logic within disciplines.
Abstract: It seems that Polish logic has always been open to considerations concerning the use of methods and results of formal logic within disciplines. We overview a couple of such Polish contributions to what may be called the realm of applied logic. We take a closer look at the formalization of natural reasoning, inconsistency-tolerant logic, and at the formal analysis of causal nexus.

1 citations

Journal ArticleDOI
TL;DR: At the end of the 1980s, Tennant invented a logical system that he called " intuitionistic relevant logic " (IR), now he calls this same system " Core logic".
Abstract: At the end of the 1980s, Tennant invented a logical system that he called " intuitionistic relevant logic " (IR, for short). Now he calls this same system " Core logic. " In Section 1, by reference to the rules of natural deduction for IR, I explain why IR is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that IR cannot be a core logic.

1 citations

Journal ArticleDOI
06 Jan 2021-Synthese
TL;DR: The purpose of this article is to argue against the notion that human reasoning is paraconsistent, as numerous findings in the area of cognitive psychology and cognitive neuroscience go against the hypothesis that humans tolerate contradictions in their inferences.
Abstract: The creation of paraconsistent logics have expanded the boundaries of formal logic by introducing coherent systems that tolerate contradictions without triviality. Thanks to their novel approach and rigorous formalization they have already found many applications in computer science, linguistics and mathematics. As a natural next step, some philosophers have also tried to answer the question if human everyday reasoning could be accurately modelled with paraconsistent logics. The purpose of this article is to argue against the notion that human reasoning is paraconsistent. Numerous findings in the area of cognitive psychology and cognitive neuroscience go against the hypothesis that humans tolerate contradictions in their inferences. Humans experience severe stress and confusion when confronted with contradictions (i.e., the so-called cognitive dissonance). Experiments on the ways in which humans process contradictions point out that the first thing humans do is remove or modify one of the contradictory statements. From an evolutionary perspective, contradiction is useless and even more dangerous than lack of information because it takes up resources to process. Furthermore, it appears that when logicians, anthropologists or psychologists provide examples of contradictions in human culture and behaviour, their examples very rarely take the form of: $$(p \wedge \lnot p)$$ . Instead, they are often conditional statements, probabilistic judgments, metaphors or seemingly incompatible beliefs. At different points in time humans are definitely able to hold contradictory beliefs, but within one reasoning leading to a particular behaviour, contradiction is never tolerated.

1 citations

Journal ArticleDOI
TL;DR: C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne, and showed that FL is the system MEN of material equivalence with negation, which accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney.
Abstract: C I Lewis showed up Down Under in 2005, in e-mails initiated by Allen Hazen of Melbourne. Their topic was the system Hazen called FL (a Funny Logic), axiomatized in passing in Lewis 1921. I show that FL is the system MEN of material equivalence with negation. But negation plays no special role in MEN. Symbolizing equivalence with → and defining ∼A inferentially as A→f, the theorems of MEN are just those of the underlying theory ME of pure material equivalence. This accords with the treatment of negation in the Abelian l-group logic A of Meyer and Slaney (Abelian logic. Abstract, Journal of Symbolic Logic 46, 425–426, 1981), which also defines ∼A inferentially with no special conditions on f. The paper then concentrates on the pure implicational part AI of A, the simple logic of Abelian groups. The integers Z were known to be characteristic for AI, with every non-theorem B refutable mod some Zn for finite n. Noted here is that AI is pre-tabular, having the Scroggs property that every proper extension SI of AI, closed under substitution and detachment, has some finiteZn as its characteristic matrix. In particular FL is the extension for which n = 2 (Lewis, The structure of logic and its relation to other systems. The Journal of Philosophy 18, 505–516, 1921; Meyer and Slaney, Abelian logic. Abstract. Journal of Symbolic Logic 46, 425–426, 1981; This is an abstract of the much longer paper finally published in 1989 in G. G. Priest, R. Routley and J. Norman, eds., Paraconsistent logic: essays on the inconsistent, Philosophica Verlag, Munich, pp. 245–288, 1989).

1 citations

Journal ArticleDOI
01 Jun 1976-Synthese
TL;DR: In this article, a method to calculate a degree of validity for the proof of a statement which is derived from empirical statements by means of logic conclusions is proposed, where the empirical statements are assumed not to be completely valid or their validity to be doubtful.
Abstract: This paper suggests a method to calculate a degree of validity for the proof of a statement which is derived from empirical statements by means of logic conclusions. The empirical statements are assumed not to be completely valid or their validity to be doubtful. The suggested rules are consistent with two-valued logic, yield decreasing validities with increasing number of applications of modus ponens and obey the law of the excluded middle. The actual calculation of validity values, the relation of the suggested method to some truth tables of multi-valued logic and to fuzzy logic are discussed.

1 citations


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