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In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs. We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of… (More)

In this paper we study fixpoints of operators on lattices and bilattices in a systematic and principled way. The key concept is that of an approximating operator, a monotone operator on the product bilattice, which gives approximate information on the original operator in an intuitive and well-defined way. With any given approximating operator our theory… (More)

In this paper, we consider the question of skeptical reasoning for an important nonmonotonic reasoning system — the autoepistemic logic of Moore. Autoepistemic logic is a method of reasoning which assigns to a set of formulas the collection of theories called stable expansions. A naive method to perform skeptical autoepistemic reasoning — deciding whether a… (More)

Autoepistemic logic is one of the principal modes of nonmonotonicreasoning. It unifies several other modes of nonmonotonic reasoning andhas important application in logic programming. In the paper, a theoryof autoepistemic logic is developed. This paper starts with a briefsurvey of some of the previously known results. Then, the nature ofnonmonotonicity is… (More)

Many nonmonotonic formalism, including default logic, logic programming with stable models, and autoepistemic logic, can be represented faithfully by means of modal nonmonotonic logics in the family proposed by McDermott and Doyle. In this paper properties of logics in this family are thoroughly investigated. We present several results on characterization… (More)

Logic programming has been introduced as programming in the Horn clause subset of first-order logic. This view breaks down for the negation as failure inference rule. To overcome the problem, one line of research has been to view a logic program as a set of iff-definitions. A second approach was to identify a unique <i>canonical, preferred</i>, or… (More)

We investigate a generalization of weight-constraint programs with stable semantics, as implemented in the ASP solver smodels. Our programs admit atoms of the form X, F where X is a finite set of propositional atoms and F is an arbitrary family of subsets of X. We call such atoms set constaints and show that the concept of stable model can be generalized to… (More)

In this paper, we describe an automated reasoning system, called DeReS. DeReS implements default logic of Reiter by supporting several basic reasoning tasks such as testing whether extensions exist, nding one or all extensions (if at least one exists) and querying if a formula belongs to one or all extensions. If an input theory is a logic program, DeReS… (More)

We revisit the issue of epistemological and semantic foundations for autoepistemic and default logics, two leading formalisms in nonmonotonic reasoning. We develop a general semantic approach to autoepistemic and default logics that is based on the notion of a belief pair and that exploits the lattice structure of the collection of all belief pairs. For… (More)