Modular semantics for theories: an approach to paraconsistent reasoning
Paraconsistent logics which avoid triviality (in which it is not the case that an arbitrary sentence can be inferred from a contradiction) have for the most part concentrated on the propositional connectives and avoided quantifiers. The present semantics focuses on dealing with inconsistencies between universally quantified or other sentences and their instances. The crucial move is that an admissible interpretation satisfies the axioms \underline{to a maximal extent}, as defined. It might be seen as an inverse to those adaptive logics which interpret existential quantifiers as being as universal as possible, by interpreting universal quantifiers as being as universal as possible while allowing exceptions. It is compared to approaches in the same field -- Priest's \textit{Chunk and Permeate}, and his \(LP^m\) -- and then applied to the inconsistent theory consisting of Bohr's postulates, classical electrodynamics, and the conservation of energy (a theory of considerable importance, both historically and pedagogically).
structuralist approach to scientific theories
scientific article; zbMATH DE number 6995844
scientific article