Open World Planning in the Situation Calculus

We describe a forward reasoning planner for open worlds that uses domain specific information for pruning its search space, as suggested by (Bacchus & Kabanza 1996; 2000). The planner is written in the situation calculus-based programming language GOLOG, and it uses a situation calculus axiomatization of the application domain. Given a sentence to prove, the planner regresses it to an equivalent sentence about the initial situation, then invokes a theorem prover to determine whether the initial database entails and hence . We describe two approaches to this theorem proving task, one based on compiling the initial database to prime implicate form, the other based on Relsat, a Davis/Putnam-based procedure. Finally, we report on our experiments with open world planning based on both these approaches to the theorem proving task. Introduction Currently, virtually all implemented deterministic planning systems make a closed world assumption that complete information is available about the initial state of the application domain. Conformant Graphplan (Smith & Weld 1998), CMBP (Cimatti & Roveri 1999) and the planner of (Rintanen 1999) are exceptions to this. So also are a few conditional planners incorporating “information gathering” actions, used to fill gaps in the planners’ incomplete knowledge base (e.g. (Golden, Etzioni, & Weld 1994; de Giacomo et al. 1997)). Open worlds preclude direct appeal to most planning algorithms in the literature, including the successful SAT (Kautz & Selman 1996) and Graphplan (Blum & Furst 1997) approaches. In this paper, we describe the theoretical foundations and implementation for an open world planner without sensing actions; its job is to find straight line plans using only what is known about the (incomplete) initial state, together with general domain specific facts like state constraints and action preconditions and effects. Ours is a forward reasoning planner, using domain dependent information to prune its search space, as suggested by (Bacchus & Kabanza 1996; 2000); it is axiomatized entirely in the situation calculus. The Situation Calculus and GOLOG The situation calculus (McCarthy 1963) is a first order language for axiomatizing dynamic worlds. In recent years, it has been considerably extended beyond the “classical” language to include concurrency, continuous time, processes, Copyright c 2000, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. sensing actions, knowledge, etc, but in all cases, its basic ingredients consist of actions, situations and fluents. Actions Actions are first order terms consisting of an action function symbol and its arguments. In the blocks world, the action of moving block onto block might be denoted by the action term . Situations A situation is a first order term denoting a sequence of actions. These sequences are represented using a binary function symbol : denotes the sequence resulting from adding the action to the sequence . So is like LISP’s