Nonmonotonic reasoning has been explored as a form of abductive reasoning where default assumptions are treated as abductive hypotheses. While the semantics and proof theories under this approach have been studied extensively , the question of how disjunctive programs may be used to reason abductively has rarely been investigated. At the center of the question is how to embed disjunctive reason...

This paper presents the relationship between disjunctive logic programs and default theories. We rst show that Bidoit and Froidevaux's positivist default theory causes a problem in the presence of disjunctive information in a program. Then we present a correct transformation of disjunctive logic programs into default theories and show a one-to-one correspondence between the stable models of a p...

We investigate the fundamental problem of when a ground atom in a disjunctive database is assumed false. There are basically two diierent approaches for inferring negative information for disjunctive databases; they are Minker's Generalized Closed World Assumption (GCWA) and Ross and Topor's Disjunctive Database Rule (DDR). A problem with the GCWA is that disjunctive clauses are sometimes inter...

We present the concept of a disjunctive basis as a generic framework for normal forms in modal logic based on coalgebra. Disjunctive bases were defined in previous work on completeness for modal fixpoint logics, where they played a central role in the proof of a generic completeness theorem for coalgebraic mu-calculi. Believing the concept has a much wider significance, here we investigate it m...

A disjunctive temporal logic programming language, called Disjunctive Chronolog is presented in this paper. Disjunctive Chronolog combines the ideas of both temporal logic programming and disjunctive logic programming. The new language is capable of expressing dynamic behaviour as well as uncertainty, two notions that are very common in a variety of real systems. Minimal model semantics, model ...

Nowadays, many real problems can be modelled as Constraint Satisfaction Problems (CSPs). Some CSPs are considered non-binary disjunctive CSPs. Many researchers study the problems of deciding consistency for Disjunctive Linear Relations (DLRs). In this paper, we propose a new class of constraints called Extended DLRs consisting of disjunctions of linear inequalities, linear disequations and non-...

This paper presents the equivalence relationship between disjunctive and abductive logic programs. We show that the generalized stable model semantics of abductive logic programs can be translated into the possible model semantics of disjunctive programs, and vice versa. It is also proved that abductive disjunctive programs can be expressed by abductive logic programs under the possible model s...

We study the problem of rewriting a disjunctive datalog program into plain datalog. We show that a disjunctive program is rewritable if and only if it is equivalent to a linear disjunctive program, thus providing a novel characterisation of datalog rewritability. Motivated by this result, we propose weakly linear disjunctive datalog—a novel rule-based KR language that extends both datalog and l...

We propose a semantics for disjunctive logic programs, based on the single notion of forcing. We show that the semantics properly extends, in a natural way, previous approaches. A fixpoint characterization is also provided. We also take a closer look at the relationship between disjunctive logic programs and disjunctivefree logic programs. We present certain criteria under which a disjunctive p...

We present a framework of logic programming using an explicit representation of defeats of assumptions, called assumption denials. We study semantics for extended, disjunctive, and extended disjunctive programs, all in the same framework. The framework is based on a x-point operator over \uninterpreted programs", and semantics for various kinds of programs are then deened simply by adding appro...