Answer Set Planning under Action Costs

We present Kc, which extends the declarative planning language K by action costs and optimal plans that minimize overall action costs (cheapest plans). As shown, this novel language allows for expressing some nontrivial planning tasks in an elegant way. Furthermore, it flexibly allows for representing planning problems under other optimality criteria as well, such as computing "fastest" plans (with the least number of steps), and refinement combinations of cheap and fast plans. Our experience is encouraging and supports the claim that answer set planning may be a valuable approach to advanced planning systems in which intricate planning tasks can be naturally specified and effectively solved.

[1]  Brian W. Kernighan,et al.  AMPL: A Modeling Language for Mathematical Programming , 1993 .

[2]  Francesco Buccafurri,et al.  Enhancing Disjunctive Datalog by Constraints , 2000, IEEE Trans. Knowl. Data Eng..

[3]  Vladimir Lifschitz,et al.  Action Languages, Answer Sets, and Planning , 1999, The Logic Programming Paradigm.

[4]  Bernhard Nebel,et al.  Encoding Planning Problems in Nonmonotonic Logic Programs , 1997, ECP.

[5]  Marco Roveri,et al.  Conformant Planning via Symbolic Model Checking , 2000, J. Artif. Intell. Res..

[6]  Carlo Zaniolo,et al.  Relating Stable Models and AI Planning Domains , 1995, ICLP.

[7]  Wolfgang Faber,et al.  Declarative problem-solving using the DLV system , 2000 .

[8]  Victor W. Marek,et al.  The Logic Programming Paradigm: A 25-Year Perspective , 2011 .

[9]  Wolfgang Faber,et al.  A logic programming approach to knowledge-state planning: Semantics and complexity , 2004, TOCL.

[10]  Francesco Buccafurri,et al.  Strong and Weak Constraints in Disjunctive Datalog , 1997, LPNMR.

[11]  Enrico Giunchiglia,et al.  An Action Language Based on Causal Explanation: Preliminary Report , 1998, AAAI/IAAI.

[12]  Mark W. Krentel.  Generalizations of Opt P to the Polynomial Hierarchy , 1992, Theor. Comput. Sci..

[13]  Enrico Giunchiglia,et al.  Planning as Satisfiability with Expressive Action Languages: Concurrency, Constraints and Nondeterminism , 2000, KR.

[14]  Henry A. Kautz,et al.  State-space Planning by Integer Optimization , 1999, AAAI/IAAI.

[15]  Vladimir Lifschitz,et al.  Representing Transition Systems by Logic Programs , 1999, LPNMR.

[16]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[17]  Kenneth A. Ross,et al.  The well-founded semantics for general logic programs , 1991, JACM.

[18]  Edwin P. D. Pednault,et al.  ADL: Exploring the Middle Ground Between STRIPS and the Situation Calculus , 1989, KR.

[19]  Hudson Turner,et al.  Satisfiability planning with Causal Theories , 1998, KR.

[20]  V. Lifschitz,et al.  Foundations of Logic Programming , 1997 .

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

[22]  Eithan Ephrati,et al.  A Cost-Directed Planner: Preliminary Report , 1996, AAAI/IAAI, Vol. 2.

[23]  Enrico Pontelli,et al.  Reasoning about Actions in Prioritized Default Theory , 2002, JELIA.

[24]  Jana Koehler,et al.  Planning under Resource Constraints , 1998, ECAI.

[25]  Alexander Nareyek.  Beyond the Plan-Length Criterion , 2000, Local Search for Planning and Scheduling.

[26]  David E. Smith,et al.  Conformant Graphplan , 1998, AAAI/IAAI.

[27]  Timo Soininen,et al.  Extending and implementing the stable model semantics , 2000, Artif. Intell..

[28]  Wolfgang Faber,et al.  Planning under Incomplete Knowledge , 2000, Computational Logic.

[29]  Steve Hanks,et al.  Optimal Planning with a Goal-directed Utility Model , 1994, AIPS.

[30]  Wolfgang Faber,et al.  Disjunctive datalog with strong and weak constraints: Representational and computational issues , 1998 .

[31]  Ilkka Niemelä,et al.  Smodels: A System for Answer Set Programming , 2000, ArXiv.

[32]  Vladimir Lifschitz,et al.  Splitting a Logic Program , 1994, ICLP.

[33]  David E. Smith,et al.  Extending Graphplan to handle uncertainty and sensing actions , 1998, AAAI 1998.

[34]  Georg Gottlob,et al.  Complexity and expressive power of logic programming , 2001, CSUR.

[35]  Blai Bonet,et al.  Planning with Incomplete Information as Heuristic Search in Belief Space , 2000, AIPS.

[36]  Enrico Giunchiglia,et al.  Representing Action: Indeterminacy and Ramifications , 1997, Artif. Intell..

[37]  Vladimir Lifschitz,et al.  Answer Set Planning (Abstract) , 1999, LPNMR.

[38]  Patrik Haslum,et al.  Admissible Heuristics for Optimal Planning , 2000, AIPS.

[39]  Enrico Giunchiglia,et al.  Planning as Satisfiability in Nondeterministic Domains , 2000, AAAI/IAAI.

[40]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

[41]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[42]  Alan L. Selman,et al.  A Taxonomy of Complexity Classes of Functions , 1994, J. Comput. Syst. Sci..

[43]  Hudson Turner,et al.  Causal Theories of Action and Change , 1997, AAAI/IAAI.