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

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 the situation calculus, and we identify and deal with three problems with his approach. Our conjecture is that our approach can be mapped back to the 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 nondetermin-istic 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 nonde-terministic actions can be specified. He then identifies a class of such actions for which regression can be used as a reasoning mechanism. Within the constraints of the SitCalc formalism, Lin provides an elegant extension to handle nondeterminism, but one can probably do somewhat better. We will show this, using PMON as a vehicle. PMON is a logic for action and change proposed by Sandewall [1994]. PMON is proven to be correctly applicable to problems involving explicit time, context-dependent actions, nondeterministic actions and actions with duration. Doherty [1994] gives a first-order formulation of PMON, with a second-order circumscription axiom and shows that it is always possible to reduce the second-order theory to first-order logic. In [Gustafsson and Doherty, 1996] PMON is further extended to handle causal constraints. In this paper we will use a subset of PMON with metric time (natural numbers) and propo-sitional fluents. There are three problems with Lin's proposal: First, he needs to explicitly enumerate all nondeterministic effects of an action in syntax, thus encountering a possible combinatorial explosion. Secondly, he has to introduce an "oracle" predicate Case, which "knows" the outcome of a nondeterministic action before it has occurred. The intuitive meaning of this oracle is unclear. Thirdly, the effects of nondeterministic actions are not allowed to depend on the situation in which the action is invoked, for regression to work properly. In PMON, we deal with each of the three problems in the following manner: The first is taken care of by the formalism, …