Possibilistic intermediate logic

摘要

We define what we call 'possibilistic intermediate logic (P1L)'; we present results analogous to those of the well-known intermediate logic, such as a deduction theorem, a generalised version of the deduction theorem, a cut rule, a weak version of a refutation theorem, a substitution theorem and Glivenko's theorem. Also, we present a definition for 'possibilistic safe beliefs'. This definition allows us to establish a relation between safe beliefs, as presented on 'applications of intuitionistic logic in answer set programming' by Osorio et al., and our version for possibilistic intermediate logic {PIL_X). We also present a characterisation of possibilistic safe beliefs for possibilistic normal logic programs.