A logic for anytime deduction and anytime compilation

One of the main characteristics of logical reasoning in knowledge based systems is its high computational complexity. Anytime deduction and anytime compilation are two attractive approaches that have been proposed for addressing such a difficulty. The first one offers a compromise between the time complexity needed to compute approximate answers and the quality of these answers. The second one proposes a trade-off between the space complexity of the compiled knowledge base and the number of possible answers that can be efficiently processed by this data structure. The purpose of this paper is to define a logic which handles these two approaches by incorporating several major features. First, the logic is semantically founded on the notion of resource which determines both the accuracy and the cost of approximation. Second, a stepwise procedure is included for improving approximate answers and allowing their convergence to the correct answer. Third, both sound approximations and complete ones are covered. Fourth and nally, the reasoning task may be done off-line and compiled theories can be used for answering many queries. This logic is applied to the specifications of anytime deducers and anytime compilers

On anytime coherence-based reasoning

Abstract. A great deal of research has been devoted to nontrivial reasoning in inconsistent knowledge bases. Coherence-based approaches proceed by a consolidation operation which selects several consistent subsets of the knowledge base and an entailment operation which uses classical implication on these subsets in order to conclude. An important advantage of these formalisms is their flexibility: consolidation operations can take into account the priorities of declarations stored in the base, and different entailment operations can be distinguished according to the cautiousness of reasoning. However, one of the main drawbacks of these approaches is their high computational complexity. The purpose of our study is to define a logical framework which handles this difficulty by introducing the concepts of anytime consolidation and anytime entailment. The framework is semantically founded on the notion of resource which captures both the accuracy and the computational cost of anytime operations. Moreover, a stepwise procedure is included for improving approximations. Finally, both sound approximations and complete ones are covered. Based on these properties, we show that an anytime view of coherence-based reasoning is tenable.