Reasoning about Action in Polynomial Time

Although many formalisms for reasoning about action exist, surprisingly few approaches have taken computational complexity into consideration. The contributions of this paper are the following: a temporal logic with a restriction for which deciding satisfiability is tractable, a tractable extension for reasoning about action, and NP-completeness results for the unrestricted problems. Many interesting reasoning problems can be modelled, involving nondeterminism, concurrency and memory of actions. The reasoning process is proved to be sound and complete. 145 1 Introduction Although many formalisms for reasoning about action exist, surprisingly few approaches have taken computational complexity into consideration. One explanation for this might be that many interesting AI problems are (at least) NP-hard, and that tractable subproblems that are easily extracted, tend to lack expressiveness. This has led a large part of the AI community to rely on heuristics and incomplete systems to s..

Reasoning by Regression: Pre- and Postdiction Procedures for Logics of Action and Change with Nondeterminism

In this paper we introduce regression-based pre- and postdiction procedures for PMON, a nonmonotonic logic for action and change with explicit time. We also provide an in depth analysis of problems with regression that occur when nondeterministic actions are introduced. We do this by employing Dijkstra's weakest liberal precondition operator, wlp. The presented work is related to recent work by Lin in situation calculus, and we identify and deal with three problems with his approach. Our conjecture is that our approach can be mapped back to situation calculus. 1 Introduction The contributions of this paper are the following: Regression-based pre- and postdiction procedures for PMON with metric time, and an in depth analysis of problems with regression that occur when nondeterministic actions are introduced. We also identify and deal with problems in previous work by Lin [ 1996 ] . Lin [ 1996 ] proposes a causal minimization framework in SitCalc (Situation Calculus), where effects of ..