Bakus How to cite this article. Let us take three vectors: One important type of paraconsistent logic is relevance logic. A wave is associated to a vector finite sequence of natural numbers xi through digital sampling. Like their biological counterparts, artificial neurons are bound together by connections that determine the fl ow of information paraconsistents peer neurons. These data are captured or received information from multiple paraconsistfnte usually comes in the form of evidence that bring many contradictions. Paraconsistent logic It is easy to check that this valuation constitutes a counterexample to both explosion and disjunctive syllogism.

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Thus if a theory contains a single inconsistency, it is trivial —that is, it has every sentence as a theorem. The characteristic or defining feature of a paraconsistent logic is that it rejects the principle of explosion.

As a result, paraconsistent logics, unlike classical and other logics, can be used to formalize inconsistent but non-trivial theories.

Comparison with classical logic[ edit ] Paraconsistent logics are propositionally weaker than classical logic ; that is, they deem fewer propositional inferences valid. The point is that a paraconsistent logic can never be a propositional extension of classical logic, that is, propositionally validate everything that classical logic does. In some sense, then, paraconsistent logic is more conservative or cautious than classical logic. It is due to such conservativeness that paraconsistent languages can be more expressive than their classical counterparts including the hierarchy of metalanguages due to Alfred Tarski et al.

According to Solomon Feferman []: " Motivation[ edit ] A primary motivation for paraconsistent logic is the conviction that it ought to be possible to reason with inconsistent information in a controlled and discriminating way. The principle of explosion precludes this, and so must be abandoned. In non-paraconsistent logics, there is only one inconsistent theory: the trivial theory that has every sentence as a theorem.

Paraconsistent logic makes it possible to distinguish between inconsistent theories and to reason with them. Research into paraconsistent logic has also led to the establishment of the philosophical school of dialetheism most notably advocated by Graham Priest , which asserts that true contradictions exist in reality, for example groups of people holding opposing views on various moral issues. For example, one need not commit to either the existence of true theories or true contradictions, but would rather prefer a weaker standard like empirical adequacy , as proposed by Bas van Fraassen.

Moreover, traditionally contradictoriness the presence of contradictions in a theory or in a body of knowledge and triviality the fact that such a theory entails all possible consequences are assumed inseparable, granted that negation is available. These views may be philosophically challenged, precisely on the grounds that they fail to distinguish between contradictoriness and other forms of inconsistency.

The very notions of consistency and inconsistency may be furthermore internalized at the object language level. Tradeoffs[ edit ] Paraconsistency involves tradeoffs. In particular, abandoning the principle of explosion requires one to abandon at least one of the following two principles: [7].


Paraconsistent logic

Als een formele wetenschap onderzoekt en classificeert de logica de structuur van beweringen en argumentaties, zowel door de studie van formele systemen van gevolgtrekking als door de studie van argumentaties in de natuurlijke taal. De studie van de logica reikt van kernzaken als de studie van drogredenen en paradoxen , tot gespecialiseerde analyse van redeneringen door gebruik van kansrekening en argumenten betreffende causaliteit. Logica wordt tegenwoordig ook gebruikt in argumentatieleer. Sinds de Middeleeuwen wordt logica bestudeerd als een vertakking van filosofie, een deel van het klassieke trivium , dat bestond uit grammatica , retorica en logica. Sinds halverwege de 19de eeuw wordt de formele logica bestudeerd in de context van de grondslagen van de wiskunde , waar het veelal symbolische logica genoemd wordt. Een van de belangrijkste notatiemethodes voor logica werd geformuleerd door Gottlob Frege , een grote inspiratiebron voor Bertrand Russell , die in samen met Alfred North Whitehead trachtte de logica formeel tot de hoeksteen van de wiskunde te ontwikkelen met de publicatie van de Principia Mathematica. In de verdere ontwikkeling van de studie van formele logica ging het onderzoek niet alleen meer over fundamentele onderwerpen.


Paraconsistent Logic

Related Entries 1. Paraconsistency is a property of a consequence relation. The role often played by the notion of consistency in orthodox logics, namely, the most basic requirement that any theory must meet, is relaxed to the notion of coherence: no theory can include every sentence whatsoever if it is to be considered tenable. Simple consistency of a theory no contradictions is a special case of absolute consistency, or non-triviality not every sentence is a part of the theory.


Paraconsistente logica



Logica paraconsistente


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