This paper discusses the resolution principle in the context of non-classical logics.

In [7] Wojtylak showed that the supremum of a finite collection of strongly finite logics is not necessarily strongly finite, putting to an end the dispute concerning the underlying algebraic structure of the set of all strongly finite logics defined on a propositional language. In this paper we prove that Wojtylak’s result extends to a wider class of propositional logics defined by finite sets of finite matrices with admissible valuations.

The properties of monotonic inference systems and the properties of their theories are strongly linked. These links, however, are much weaker in nonmonotonic inference systems. In this paper we introduce the notion of anaxiomatic variety for a theory and show how this notion, instead of the notion of a theory, can be used for the syntactic and semantic analysis of nonmonotonic inferences.

A proof-theoretical analysis of finite-valuedness in the domain of cumulative inference systems is presented.