A Proof-Theoretic Approach to Irrelevance: Foundations and Applications

Control of reasoning isa major issue in scaling up problem solvers that use declarative representations, since inference isslowed own significantly as the size of the knowledge base (KB) is increased. A key factor for the slow down is the search of the inference engine through parts of the KB that are irrelevant to the query at hand. The ability of a system to ignore irrelevant information is therefore a key in scaling up AI systems to large and complex domains. To address this problem we have developed a general framework for analyzing irrelevance and specific algorithms for efficiently detecting irrelevant portions of a knowledge base [Levy, 1993]. Our framework focussed on the following problem. Given a knowledge base A and a query q, which parts of A are irrelevant to q, and how can the problem solver use this knowledge of irrelevance to improve its performance. Since our main goal in analyzing irrelevance was to speed up inference, we presented a proof theoretic analysis of irrelevance, as opposed to attempts oformalize the common sense notion of irrelevance [Keynes, 1921; Carnap, 1950; GKrdenfors, 1978], or a meta-theoretic analysis [Subramanian, 1989]. In our analysis we presented a space of possible d finitions f irrelevance and analyzed the properties ofdefinitions in the space. We have shown that the proof theoretic analysis yields the necessary distinctions that enable us to address the issues concerning the usage of irrelevance to speed up inferences. The space of definitions provided several insights onthe kinds of irrelevancies thatarise in inference, on the utility of ignoring irrelevant information, and on problems that seemed previously unrelated. A key component of our work addressed the issue of developing efficient algorithms for automatically detecting irrelevant parts of a knowledge base [Levy and Sagiv, 1992; Levy et al., 1993; Levy and Sagiv, 1993; Levy et al., 1994a]. Our work yielded solutions toseveral open theoretical problems, aswell as practical gorithms which are now being incorporated into commercial database systems. We have also applied our framework to the problems of automatically creating abstractions [Levy, 1994], creating models for physical devices (for tasks uch as design, simulation a d diagnosis) [Iwasaki and Levy, 1994J, and gathering information in distributed heterogeneous environments [Levy et al., 1994b]. This paper focuses on the foundations of our framework and outlines the space of definitions of irrelevance. The last section outlines the results concerning automatic determination of irrelevance and describes the applications of our framework.