In recent years, much work was devoted to the study of theoretical foundations of Disjunctive Logic Programming and Disjunctive Deductive Databases. While the semantics of non-disjunctive programs is fairly well understood, the declarative and computational foundations of disjunctive logic programming proved to be much more elusive and diicult. Recently, two new and promising semantics have bee...

Nowadays, many researchers are working on Constraint Satisfaction Problems (CSPs). Many CSPs can be modelled as non-binary CSPs and, theoretically, they can be transformed into an equivalent binary CSP, using some of the current techniques. However, this transformation may be an inadequate or inefficient way to manage certain types of non-binary constraints. In this paper, we propose an algorit...

Set-valued information systems are generalized models of single-valued information systems. Its semantic interpretation can be classified into two categories: disjunctive and conjunctive. We focus on the former in this paper. By introducing four types of dominance relations to the disjunctive set-valued information systems, we establish a dominance-based rough sets approach, which is mainly bas...

We propose three equivalent domain-theoretic semantics for dis-junctive logic programs in the style of Gelfond and Lifschitz. These are (i) a resolution-style inference semantics; (ii) a model-theoretic semantics; and (iii) a (nondeterministic) state-transition semantics. We show how these three semantics generalize \for free" to disjunctive logic programming over any Scott domain. We also rela...

Ali Enayat had asked whether two halves of Disjunctive Correctness (DC) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that principle “every true disjunction has a disjunct” is equivalent to bounded induction and thus it not conservative. On other hand, converse implication “any with disjunct true” can be conservatively added PA. The me...