David Poole's Specificity Revised

TL;DR

This paper revises David Poole's original notion of specificity in AI, addressing its complexity and transitivity issues, and proposes a closer approximation to human intuition with some mathematical insights.

Contribution

It introduces a new specificity ordering that better aligns with human intuition and clarifies the non-transitivity of Poole's relation, with implications for non-monotonic reasoning.

Findings

Poole's relation is not transitive.

The new specificity ordering aligns better with human intuition.

Deciding the new relation is only slightly more efficient.

Abstract

In the middle of the 1980s, David Poole introduced a semantical, 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 ordering 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. The present means to decide our novel specificity relation, however, show only a slight improvement over the known ones for Poole's relation, and further work is needed in this aspect.