Modelling default and likelihood reasoning as probabilistic reasoning

This paper presents a probabilistic analysis of plausible reasoning about defaults and about likelihood. "Likely" and "by default" are in fact treated as duals in the same sense as "possibility" and "necessity". To model these four forms probabilistically, a logic QDP and its quantitative counterpart DP are derived that allow qualitative and corresponding quantitative reasoning. Consistency and consequence results for subsets of the logics are given that require at most a quadratic number of satisfiability tests in the underlying prepositional logic. The quantitative logic shows how to track the propagation error inherent in these reasoning forms. The methodology and sound framework of the system highlights their approximate nature, the dualities, and the need for complementary reasoning about relevance.