Showing papers by "Hector J. Levesque published in 2006"

On the limits of planning over belief states under strict uncertainty

Abstract: A recent trend in planning with incomplete information is to model the actions of a planning problem as non-deterministic transitions over the belief states of a planner, and to search for a plan that terminates in a desired goal state no matter how these transitions turn out. We show that this view of planning is fundamentally limited. Any plan that is successful by this criteria has an upper bound on the number of actions it can execute. Specifically, the account will not work when iterative plans are needed. We also show that by modifying the definition slightly, we obtain another account of planning that does work properly even for iterative plans. Although the argument is presented in an abstract form, we illustrate the issues using a simple concrete example.

Towards an axiom system for default logic

Abstract: Recently, Lakemeyer and Levesque proposed a logic of only-knowing which precisely captures three forms of nonmonotonic reasoning: Moore's Autoepistemic Logic, Konolige's variant based on moderately grounded expansions, and Reiter's default logic. Defaults have a uniform representation under all three interpretations in the new logic. Moreover, the logic itself is monotonic, that is, nonmonotonic reasoning is cast in terms of validity in the classical sense. While Lakemeyer and Levesque gave a model-theoretic account of their logic, a proof-theoretic characterization remained open. This paper fills that gap for the propositional subset: a sound and complete axiom system in the new logic for all three varieties of default reasoning. We also present formal derivations for some examples of default reasoning. Finally we present evidence that it is unlikely that a complete axiom system exists in the first-order case, even when restricted to the simplest forms of default reasoning.

The Truth about Defaults

Abstract: It is a great honour and a pleasure to be able to offer this paper in celebration of Vladimir Lifschitz's sixty-fifth birthday. His work has been an inspiration to both of us since we first started reading his papers in the 1980s. At a time when many papers and presentations in AI were either very abstract on the one hand, or tied to specific systems on the other, Vladimir has consistently found a sweet spot that emphasized clarity and rigour, while maintaining a strong connection to AI practice. His work, in a nutshell, has been a model of how to do AI research, of great value to new students and to older researchers like us. So this is our chance to say thank you, Vladimir, and happy birthday!