Paraconsistency in Categories: Case of Relevance Logic

Abstract

Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.

Логический Плюрализм И Неклассическая Теория Категорий

“…Теперь, строя топос Set C , мы получаем интерпретацию формул паранепротиворечивой логики да Косты C 1 ,которая будет основана на Set C -оценке, представляющей собой функцию V : Φ 0 → Set C (1, Ω), сопоставляющую каждой пропозициональной переменной π i некоторое истинностное значение V (π i ) = 1 Ω (см. [14]).…”

On a paraconsistentization functor in the category of consequence structures

“…The aim is to get a general, unified and abstract perspective by means of a functor from the category of explosive logics (accepting ex falso) to the category of non-explosive logics (rejecting ex falso). The idea of using category theory to reason about logic is very popular recently, but studies connecting paraconsistency and categories are rare, and we could mention, for instance, the case of [19] and also [13].…”