Saturation, nonmonotonic reasoning and the closed-world assumption
Artificial Intelligence
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Forcing versus closed world assumption
Proceedings of the Second International Symposium on Methodologies for intelligent systems
Foundations of deductive databases and logic programming
Foundations of deductive databases and logic programming
Towards a theory of declarative knowledge
Foundations of deductive databases and logic programming
On the relationship between circumscription and negation as failure
Artificial Intelligence
First-order logic and automated theorem proving
First-order logic and automated theorem proving
Closed world data bases with views
Methodologies for intelligent systems, 5
Preservation properties in deductive databases
Methods of Logic in Computer Science
Evaluation of Queries under Closed-World Assumption
Journal of Automated Reasoning
Incremental models of updating data bases
Proceedings of the Conference on Algebraic Logic and Universal Algebra in Computer Science
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This paper constitutes the second part of a paper published in the iJournal of Automated Reasoning 18 (1997), 357–398.The minimal entailment ⊢iM i n has been characterized elsewhere by iP ⊢iM i n ϕ iff iC n(iP ∪{ϕ}) ∩ iG P o s ⊆ iC n(iP), where iC n is the first-order consequence operation, iP is a set of clauses (disjunctive logic program; in short: a program), ϕ is a clause (a query), and iG P o s is the set of positive (that is, bodiless) ground clauses. In this part, we address the problem of computational feasibility of certain iterative applications of criterion (1).In the first part of the paper we proposed a query evaluation algorithm that decided iP ⊢iM i n ϕ by what we called indefinite modeling. The query evaluation algorithm was capable of deciding the right-hand side of (1) without actually computing all ground positive consequences of iP or iP ∪{ϕ}. The objective of the second part of the paper is to extend the proposed approach so that it properly captures phenomena associated with allowing negation in clauses" bodies, however, at a price of substantial complication (in particular, computing all ground positive consequences of iP ∪{ϕ} that are not consequences of iP can no longer be avoided). For that purpose, we introduce the concepts of a layered program and its hierarchically minimal semantics, a special case of which covers stratified programs with semantics defined by second-order prioritized circumscription and, in the case of definite programs, perfect models. We characterize the hierarchically minimal entailment ⊢iH M i n in terms of iterative application of the right-hand side of criterion (1). Finally, we generalize the indefinite modeling and query evaluation algorithms presented in Part I over the layered programs, and indicate their computational advantages relative to other methods (e.g., those based on prefect model semantics). The presented approach does not require assigning different meanings to logically equivalent clauses, so it actually eliminates the need for program clauses with negation in their bodies.