Towards a characterization of semi-stable models in the logic of here-and-there

Abstract

The main motivation for any paraconsistent logic is the idea that reasoning with inconsistent information should be allowed and possible in a controlled and discriminating way. The principle of explosion makes this inviable, and as such must be abandoned. In non-paraconsistent logics, only one inconsistent theory exists: the trivial theory that contains every sentence as a theorem. Paraconsistent logic allows distinguishing between inconsistent theories and to reason with them. Sometimes it is possible to revise a theory to make it consistent, however in other cases (e.g., large software systems) it is currently impossible to attain consistency. Some philosophers and logicians take a radical approach, holding that some contradictions are true, and thus a theory being inconsistent is not something undesirable.<br />We characterize and present a new way of calculating semi-stable models models of a program which are paraconsistent in the presence of incoherence, without having to explicitly perform a syntactical transformation as the epistemic transformation presented in the original definition. We do this by dealing with strong negation and then calculating the program's Routley models. Afterwards we need only perform a selection according to criteria we characterize in this document.