The Complexity of Restricted Consequence Finding and Abduction

Abstract

We analyze the complexity of propositional kernel resolution (del Val 1999), a general method for obtaining logical consequences in restricted target languages. Di#erent choices of target are relevant to important AI tasks, e.g. prime implicates, satisfiability, abduction and non-monotonic reasoning, and polynomial-size knowledge compilation. Based on a generalized concept of induced width, we identify new tractable classes for various targets, and show how to estimate in advance the complexity of every problem, under various atom orderings. This can be used to choose an ordering for kernel resolution. Two applications are discussed: estimating the number of prime implicates of any theory; and identifying tractable abduction and diagnosis problems. Introduction Kernel resolution (del Val 1999) is a powerful method for generating consequences of a logical theory, where we can restrict in arbitrary ways which consequences we are interested in by looking only for consequences in some "ta...