The Common Order-Theoretic Structure of Version Spaces and ATMS\u27s

This paper exposes the common order-theoretic properties of the structures manipulated by the version space algorithm [Mit78]and the assumption-based truth maintenance systems (ATMS) [dk86a,dk86b] by recasting them in the framework of convex spaces. Our analysis of version spaces in this framework reveals necessary and sufficient conditions for ensuring the preservation of an essential finite representability property in version space merging. This analysis is used to formulate several sufficient conditions for when a language will allow version spaces to be represented by finite sets of concepts (even when the universe of concepts may be infinite). We provide a new convex space based formulation of computation performs by an ATMS which extends the expressiveness of disjunctions in the systems. This approach obviates the need for hyper-resolution in dealing with disjunction and results in simpler label-update algorithms

Focusing ATMS Problem-Solving: A Formal Approach

The Assumption-based Truth Maintenance System (ATMS) is a general and powerful problem-solving tool in AI. Unfortunately, its generality usually entails a high computational cost. In this paper, we study how a general notion of cost function can be incorporated into the design of an algorithm for focusing the ATMS, called BF-ATMS. The BF-ATMS algorithm explores a search space of size polynomial in the number of assumptions, even for problems which are proven to have exponential size labels. Experimental results indicate significant speedups over the standard ATMS for such problems. In addition to its improved efficiency, the BF-ATMS algorithm retains the multiple-context capability of an ATMS, and the important properties of consistency, minimality, soundness, as well as the property of bounded completeness. The usefulness of the new algorithm is demonstrated by its application to the task of consistency-based diagnosis, where dramatic efficiency improvements, with respect to the standard solution technique, are obtained