A series of revisions of David Poole’s specificity

Abstract

In the middle of the 1980s, David Poole introduced a semantic, model-theoretic notion of specificity to the artificial-intelligence community. Since then it has found further applications in non-monotonic reasoning, in particular in defeasible reasoning. Poole tried to approximate the intuitive human concept of specificity, which seems to be essential for reasoning in everyday life with its partial and inconsistent information. His notion, however, turns out to be intricate and problematic, which -- as we show -- can be overcome to some extent by a closer approximation of the intuitive human concept of specificity. Besides the intuitive advantages of our novel specificity orderings over Poole's specificity relation in the classical examples of the literature, we also report some hard mathematical facts: Contrary to what was claimed before, we show that Poole's relation is not transitive in general. The first of our specificity orderings (CP1) captures Poole's original intuition as close as we could get after the correction of its technical flaws. The second one (CP2) is a variation of CP1 and presents a step toward similar notions that may eventually solve the intractability problem of Poole-style specificity relations. The present means toward deciding our novel specificity relations, however, show only slight improvements over the known ones for Poole's relation; therefore, we suggest a more efficient workaround for applications in practice.