Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many...

The monadic fragments of first-order Gödel logics are investigated. It is shown that all finite-valued monadic Gödel logics are decidable; whereas, with the possible exception of one (G↑), all infinitevalued monadic Gödel logics are undecidable. For the missing case G↑ the decidability of an important sub-case, that is well motivated also from an application oriented point of view, is proven. A...

Abstract: Methods for solution of a large class of problems on the base of nonclassical, multiple-valued, and probabilistic logics have been discussed. A theory of knowledge about changing knowledge, of defeasible inference, and network approach to an analogous derivation have been suggested. A method for regularity search, logic-axiomatic and logic-probabilistic methods for learning of terms a...

In this paper we study frame definability in finitely valued modal logics and establish two main results via suitable translations: (1) one cannot define more classes of frames than are already definable classical logic (cf. [27, Thm. 8]), (2) a large family exactly the same as (including based on finite Heyting MV-algebras, or even BL-algebras). way may observe, for example, that celebrated Go...