Encoding Plans in Propositional Logic

In recent work we showed that planning problems can be efficiently solved by general propositional satisfiability algorithms (Kautz and Selman 1996). A key issue in this approach is the development of practical reductions of planning to SAT. We introduce a series of different SAT encodings for STRIPS-style planning, which are sound and complete representations of the original STRIPS specification, and relate our encodings to the Graphplan system of Blum and Furst (1995). We analyze the size complexity of the various encodings, both in terms of number of variables and total length of the resulting formulas. This paper complements the empirical evaluation of several of the encodings reported in Kautz and Selman (1996). We also introduce a novel encoding based on the theory of causal planning, that exploits the notion of “lifting” from the theorem-proving community. This new encoding strictly dominates the others in terms of asymptotic complexity. Finally, we consider further reductions in the number of variables used by our encodings, by compiling away either statevariables or action-variables.

[1]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[2]  Richard Fikes,et al.  STRIPS: A New Approach to the Application of Theorem Proving to Problem Solving , 1971, IJCAI.

[3]  Mike Paterson,et al.  Linear unification , 1976, STOC '76.

[4]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[5]  A. Haas.  The Case for Domain-Specific Frame Axioms , 1987 .

[6]  Lenhart K. Schubert.  Monotonic Solution of the Frame Problem in the Situation Calculus: An Efficient Method for Worlds wi , 1990 .

[7]  David A. McAllester,et al.  Systematic Nonlinear Planning , 1991, AAAI.

[8]  Tom Bylander,et al.  Complexity Results for Planning , 1991, IJCAI.

[9]  Hector J. Levesque,et al.  A New Method for Solving Hard Satisfiability Problems , 1992, AAAI.

[10]  Manuela Veloso.  Learning by analogical reasoning in general problem-solving , 1992 .

[11]  Bart Selman,et al.  Planning as Satisfiability , 1992, ECAI.

[12]  Daniel S. Weld,et al.  UCPOP: A Sound, Complete, Partial Order Planner for ADL , 1992, KR.

[13]  V. S. Subrahmanian,et al.  On the Complexity of Domain-Independent Planning , 1992, AAAI.

[14]  Christer Backstrom,et al.  Computational Complexity of Reasoning about Plans , 1992 .

[15]  Dana S. Nau,et al.  On the Complexity of Blocks-World Planning , 1992, Artif. Intell..

[16]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[17]  James M. Crawford,et al.  Experimental Results on the Crossover Point inSatis ability , 1993 .

[18]  Bart Selman,et al.  Local search strategies for satisfiability testing , 1993, Cliques, Coloring, and Satisfiability.

[19]  Daniel S. Weld,et al.  Partial-Order Planning: Evaluating Possible Efficiency Gains , 1994, Artif. Intell..

[20]  Manuela M. Veloso,et al.  The Need for Different Domain-independent Heuristics , 1994, AIPS.

[21]  Bart Selman,et al.  Near-Optimal Plans, Tractability, and Reactivity , 1994, KR.

[22]  Avrim Blum,et al.  Fast Planning Through Planning Graph Analysis , 1995, IJCAI.

[23]  Bart Selman,et al.  Pushing the Envelope: Planning, Propositional Logic and Stochastic Search , 1996, AAAI/IAAI, Vol. 2.

[24]  Martha E. Pollack,et al.  Passive and active decision postponement in plan generation , 1996 .

[25]  John K. Slaney,et al.  Linear Time Near-Optimal Planning in the Blocks World , 1996, AAAI/IAAI, Vol. 2.

[26]  Fahiem Bacchus,et al.  Using temporal logic to control search in a forward chaining planner , 1996 .

[27]  Subbarao Kambhampati,et al.  On the Role of Disjunctive Representations and Constraint Propagation in Refinement Planning , 1996, KR.