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FC-normal logic programs are a generalization by Marek, Nerode, and Remmel of Reiter’s normal default theories. They have the property that, unlike most logic programs, they are guaranteed to have simple stable models. In this paper it is shown that the problem of skeptical reasoning in FC-normal programs is Π1-complete, the same complexity as for logic programs without the restriction of FC-no...

There are a wide variety of applications that either require or assume the existence of some underlying definition of “interestingness.” However, interests vary from user to user, from situation to situation, and from one time to another. This diversity of interests cannot be captured through a single definition. In this paper, we propose a framework called Full Interestingness Programs (FIPs) ...

In this paper, we consider a method of computing minimal models in circumscription using integer programming in propositional logic and first-order logic with domain closure axioms and unique name axioms. This kind of treatment is very important since this enable to apply various technique developed in operations research to nonmonotonic reasoning. (Nerode et al., 1995) are the first to propose...

Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage of a given language. In this paper we present a new characterization of relative observability, based on which an operator on languages is proposed whose la...

In this paper, we establish the concept of regularity for languages consisting of Message Sequence Charts (MSCs). To this aim, we formalise their behaviour by string languages and give a natural definition of regularity in terms of an appropriate Nerode right congruence. Moreover, we present a class of accepting automata and, using this characterisation, establish several decidability and closu...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.