A Reasoning System for a First-Order Logic of Limited Belief
This work addresses the practical implementation gap for logics of limited belief, which could benefit AI systems requiring efficient reasoning in complex domains.
The paper tackles the problem of computationally feasible reasoning in expressive first-order logic by developing a logic of limited belief that is decidable in first-order and tractable in propositional cases, and introduces a reasoning system with experimental results showing benefits.
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning decidable or even tractable. While a number of such logics have been proposed in the past, they tend to remain for theoretical analysis only and their practical relevance is very limited. In this paper, we aim to go beyond the theory. Building on earlier work by Liu, Lakemeyer, and Levesque, we develop a logic of limited belief that is highly expressive while remaining decidable in the first-order and tractable in the propositional case and exhibits some characteristics that make it attractive for an implementation. We introduce a reasoning system that employs this logic as representation language and present experimental results that showcase the benefit of limited belief.