Paraconsistency in categories: case of relevance logic. (English) Zbl 1248.03041
Summary: A category-theoretic semantics for 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 special endofunctors) in the category of sets. The completeness of the relevant system R of entailment is proved with respect to the semantics considered.
MSC:
| 03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) |
| 03B53 | Paraconsistent logics |
| 03G30 | Categorical logic, topoi |
| 18B25 | Topoi |
Keywords:
relevant algebra; RN-categories; topos of functors; interpretation of relevance logic in a topos; completeness of logic RLReferences:
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