The Common Order - Theoretic Structure

We demonstrate how order-theoretic abstractions can be useful in identifying , formalizing, and exploiting relationships between seemingly dissimilar AI algorithms that perform computations on partially-ordered sets. In particular, we show how the order-theoretic concept of an anti-chain can be used to provide an eecient representation for such sets when they satisfy certain special properties. We use anti-chains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm 10] and the assumption-based truth maintenance system (ATMS) 2, 3]. Our analysis allows us to (1) extend the known theory 7, 10, 8] of admissibility of concept spaces for incremental version space merging, and (2) develop new, simpler label-update algorithms for ATMS's with DNF assumption formulas.