An important limitation of traditional logic programming as a knowledge representation tool, in comparison with classical logic, is that logic programming does not allow us to deal directly with incomplete information. In order to overcome this limitation, we extend the class of general logic programs by including classical negation, in addition to negation-as-failure. The semantics of such extended programs is based on the method of stable models. The concept of a disjunctive database can be extended in a similar way. We show that some facts of commonsense knowledge can be represented by logic programs and disjunctive databases more easily when classical negation is available. Computationally, classical negation can be eliminated from extended programs by a simple preprocessor. Extended programs are identical to a special case of default theories in the sense of Reiter. 1 Introduction An important limitation of traditional logic programming as a knowledge representation tool, in comp...

Abstract not found

In this paper we study the properties of the class of head-cycle-free extended disjunctive logic programs (HEDLPs), which includes, as a special case, all nondisjunctive extended logic programs. We show that any propositional HEDLP can be mapped in polynomial time into a propositional theory such that each model of the latter corresponds to an answer set, as defined by stable model semantics, of the former. Using this mapping, we show that many queries over HEDLPs can be determined by solving propositional satisfiability problems. Our mapping has several important implications: It establishes the NP-completeness of this class of disjunctive logic programs; it allows existing algorithms and tractable subsets for the satisfiability problem to be used in logic programming; it facilitates evaluation of the expressive power of disjunctive logic programs; and it leads to the discovery of useful similarities between stable model semantics and Clark's predicate completion. 1 Introduction ...

. At a workshop held in Toulouse, France in 1977, Gallaire, Minker and Nicolas stated that logic and databases was a field in its own right (see [131]). This was the first time that this designation was made. The impetus for this started approximately twenty years ago in 1976 when I visited Gallaire and Nicolas in Toulouse, France, which culminated in a workshop held in Toulouse, France in 1977. It is appropriate, then to provide an assessment as to what has been achieved in the twenty years since the field started as a distinct discipline. In this retrospective I shall review developments that have taken place in the field, assess the contributions that have been made, consider the status of implementations of deductive databases and discuss the future of work in this area. 1 Introduction As described in [234], the use of logic and deduction in databases started in the late 1960s. Prominent among the developments was the work by Levien and Maron [202, 203, 199, 200, 201] and Kuhns [1...

. We present a bottom-up algorithm for the computation of the well-founded model of non-disjunctive logic programs. Our method is based on the elementary program transformations studied by Brass and Dix [6, 7]. However, their "residual program" can grow to exponential size, whereas for function-free programs our "program remainder " is always polynomial in the size, i.e. the number of tuples, of the extensional database (EDB). As in the SLG-resolution of Chen and Warren [11, 12, 13], we do not only delay negative but also positive literals if they depend on delayed negative literals. When disregarding goal-directedness, which needs additional concepts, our approach can be seen as a simplified bottom-up version of SLG-resolution applicable to range-restricted Datalog programs. Since our approach is also closely related to the alternating fixpoint procedure [27, 28], it can possibly serve as a basis for an integration of the resolution-based, fixpoint-based, and transformation-based ev...

Abstract not found

This paper investigates the problem of finding subclasses of nonmonotonic reasoning which can be implemented efficiently. The ability to "define" propositions using default assumptions about the same propositions is identified as a major source of computational complexity in nonmonotonic reasoning. If such constructs are not allowed, i.e. stratied knowledge bases are considered, a significant computational advantage is obtained. This is demonstrated by developing an iterative algorithm for propositional stratified autoepistemic theories the complexity of which is dominated by required classical reasoning. Thus efficient subclasses of stratied nonmonotonic reasoning can be obtained by further restricting the form of sentences in a knowledge base. As an example quadratic and linear time algorithms for specific subclasses of stratified autoepistemic theories are derived. The results are shown to imply efficient reasoning methods for stratied cases of default logic, logic programs, truth maintenance systems, and nonmonotonic modal logics.

The use of explicit negation enhances the expressive power of logic programs by providing a natural and unambiguous way to assert negated information about the domain being represented. We study the semantics of disjunctive programs that contain both explicit negation and negationby -default, called extended disjunctive logic programs. General techniques are described for extending model, fixpoint, and proof theoretic characterizations of an arbitrary semantics of normal disjunctive logic programs to cover the class of extended programs. Illustrations of these techniques are given for stable models, disjunctive well-founded and stationary semantics. The declarative complexity of the extended programs, as well as the algorithmic complexity of the proof procedures and fixpoint operators, are discussed. 1 Introduction The purpose of this paper is to study, in a comprehensive manner, different aspects of extended disjunctive logic programs (edlps for short), that is, programs whose clause...

in my opinion, it

www.rthomaso.eecs.umich.edu