We present here a new formalization of beliefs, which has a simpler semantics than the previous formalizations, and develop an inference method for it by generalizing the resolution method. The usual prepositional formulas are embedded in our logic as a special type of belief formulas. One can obtain a non-monotonic logic of beliefs by applying, say, circumscription to the basic belieflogic dev...

We show that the concept of strong equivalence of logic programs can be generalized to an abstract algebraic setting of operators on complete lattices. Our results imply characterizations of strong equivalence for several nonmonotonic logics including logic programming with aggregates, default logic and a version of autoepistemic logic.

The model theory of a first-order logic called N is introduced. N does not eliminate double negations, as classical logic does, but instead reduces fourfold negations. N is very close to classical logic: N has two truth values; implications are, in N like in classical logic, material; and negation distributes over compound formulas in N as it does in classical logic. Results suggest that the se...

When I started out as a newly hatched PhD student, back in the day, one of the first articles I read and understood (or at least thought that I understood) was Ray Reiter's classic article on default logic (Reiter, 1980). This was some years after the famous 'non-monotonic logic' issue of Artificial Intelligence in which that article appeared, but default logic was still one of the leading appr...

The aim of this paper is to compare first order predicate logic, fuzzy logic and non-monotonic logic as knowledge representation methods. First, we define five properties of knowledge; conceptualization, transfer, modification, integration and decomposition. We also evaluate first order predicate logic, fuzzy logic and non-monotonic logic for the above properties, in the view of accuracy, compl...

Abstract. The agent paradigm, commonly implemented by means of imperative languages mainly for reasons of efficiency, has recently increased its influence in the research and development of computational logic based systems. Since efficiency is not always the crucial issue, but clear specification and correctness is, Logic Programming and Non-monotonic Reasoning have been brought back into the ...

\It seems to me, that work in databases, logic programming, deductive databases, artii-cial intelligence and expert systems will move closer towards one another. Formalisms and techniques developed in each one of those areas will assist the others. Science builds on theories." | J. Minker, 1987

In this position paper we reconstruct and evaluate three arguments by Jean-Yves Béziau put forward to show that paraconsistent logics may replace non-monotonic logics in the analysis of situations what the latter were created for, namely updating of databases by increment of information. As originally put forward they might seem too colorful or unserious and easily dismissible, but they really ...

Current research on non-monotonic reasoning shows growing interest on implementation details, so the need for concrete calculi formalizing non-monotonic logics is clearly recognized. On the other hand, there is also an increased number of works combining intuitionistic logic with various kinds of non-monotonic formalisms. As a case in point, intuitionistic versions of both default and autoepist...

Non-monotonic inference is inference that is defeasible: in contrast with deductive inference, the conclusions drawn may be withdrawn in the light of further information, even though all the original premises are retained. Much of our everyday reasoning is like this, and a non-monotonic approach has applications to a number of technical problems in artificial intelligence. Work on formalizing n...