Category:Paraconsistent Logic

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Paraconsistent Logic

"

The contemporary logical orthodoxy has it that, from contradictory premises, anything can be inferred. Let ⊨ be a relation of logical consequence, defined either semantically or proof-theoretically. Call ⊨ explosive if it validates {A , ¬A} ⊨ B for every A and B (ex contradictione quodlibet (ECQ)). Classical logic, and most standard ‘non-classical’ logics too such as intuitionist logic, are explosive. Inconsistency, according to received wisdom, cannot be coherently reasoned about.

Paraconsistent logic challenges this orthodoxy. A logical consequence relation, ⊨, is said to be paraconsistent if it is not explosive. Thus, if ⊨ is paraconsistent, then even if we are in certain circumstances where the available information is inconsistent, the inference relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a sensible manner that treats inconsistent information as informative. The prefix ‘para’ in English has two meanings: ‘quasi’ (or ‘similar to, modelled on’) or ‘beyond’. When the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976, he seems to have had the first meaning in mind. Many paraconsistent logicians, however, have taken it to mean the second, which provided different reasons for the development of paraconsistent logic as we will see below. " - Plato Stanford Encyclopaedia of Philosophy

Subcategories

This category has the following 2 subcategories, out of 2 total.

Pages in category ‘Paraconsistent Logic’

The following 5 pages are in this category, out of 5 total.