Skip to main content
×
Home

ASPeRiX, a first-order forward chaining approach for answer set computing*

  • CLAIRE LEFÈVRE (a1), CHRISTOPHER BÉATRIX (a1), IGOR STÉPHAN (a1) and LAURENT GARCIA (a1)
Abstract
Abstract

The natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first-order logic program with default negation. In a preliminary step, this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (stable models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation. In this article, the project ASPeRiX. is presented as a first-order forward chaining approach for Answer Set Computing. This project was among the first to introduce an approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. The methodology applies a forward chaining of first-order rules that are grounded on the fly by means of previously produced atoms. Theoretical foundations of the approach are presented, the main algorithms of the ASP solver ASPeRiX. are detailed and some experiments and comparisons with existing systems are provided.

Copyright
Footnotes
Hide All
*

This work was supported by ANR (National Research Agency), project ASPIQ under the reference ANR-12-BS02-0003.

Footnotes
References
Hide All
Alviano M., Calimeri F., Faber W., Ianni G. and Leone N. 2011. Function symbols in ASP: Overview and perspectives. In Nonmonotonic Reasoning, Essays Celebrating its 30th Anniversary, Vol. 31, Brewka G., Marek V., and Truszczynski M., Eds. Studies in Logic, College Publications, 124.
Alviano M., Dodaro C., Faber W., Leone N. and Ricca F. 2013. WASP: A native ASP solver based on constraint learning. In Proc. of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'13), Cabalar P. and Son T. C., Eds. LNCS, vol. 8148. Springer, 5567.
Alviano M., Faber W. and Leone N. 2010. Disjunctive ASP with functions: Decidable queries and effective computation. Theory and Practice of Logic Programming 10 (4–6), 497512.
Balduccini M. 2009. Representing constraint satisfaction problems in answer set programming. In Proc. of the Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP'09). Faber W. and Lee J., Eds. 16–30.
Baral C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.
Baselice S., Bonatti P. and Gelfond M. 2005. Towards an integration of answer set and constraint solving. In Proc. of the 21st International Conference on Logic Programming (ICLP'05), Gabbrielli M. and Gupta G., Eds. LNCS, vol. 3668. Springer, 5266.
Baselice S. and Bonatti P. A. 2010. A decidable subclass of finitary programs. Theory and Practice of Logic Programming 10 (4–6), 481496.
Buccafurri F., Leone N. and Rullo P. 2000. Enhancing disjunctive datalog by constraints. IEEE Transactions on Knowledge and Data Engineering 12 (5), 845860.
Calimeri F., Cozza S., Ianni G. and Leone N. 2008. Computable functions in ASP: Theory and implementation. In Proc. of the 24th International Conference on Logic Programming (ICLP'08), de la Banda M. G. and E. Pontelli, Eds. LNCS, vol. 5366. Springer, 407424.
Calimeri F., Cozza S., Ianni G. and Leone N. 2011. Finitely recursive programs: Decidability and bottom-up computation. AI Communications 24 (4), 311334.
Calimeri F., Ianni G. and Ricca F. 2014. The third open answer set programming competition. Theory and Practice of Logic Programming 14 (1), 117135.
Calimeri F., Perri S. and Ricca F. 2008. Experimenting with parallelism for the instantiation of ASP programs. Journal of Algorithms 63 (1–3), 3454.
Dal Palù A., Dovier A., Pontelli E. and Rossi G. 2009. Gasp: Answer set programming with lazy grounding. Fundamenta Informaticae 96 (3), 297322.
Dao-Tran M., Eiter T., Fink M., Weidinger G. and Weinzierl A. 2012. OMiGA: An open minded grounding on-the-fly answer set solver. In Proc. of the 13th European Conference on Logics in Artificial Intelligence (JELIA'12), Luis Fariñas del Cerro, Andreas Herzig and Jérôme Mengin, Eds. LNAI, vol. 7519. Springer, 480483.
Eiter T., Lu J. J. and Subrahmanian V. S. 1997. Computing non-ground representations of stable models. In Proc. of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'97), Dix J., Furbach U., and Nerode A., Eds. LNCS, vol. 1265. Springer, 198217.
Faber W., Leone N. and Perri S. 2012. The intelligent grounder of DLV. In Correct Reasoning - Essays on Logic-Based AI in Honour of Vladimir Lifschitz, Erdem E., Lee J., Lierler Y., and Pearce D., Eds. LNCS, vol. 7265. Springer, 247264.
Faber W., Leone N. and Pfeifer G. 1999. Pushing goal derivation in dlp computations. In Proc. of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'99), Gelfond M., Leone N. and Pfeifer G., Eds. LNCS, vol. 1730. Springer, 177191.
Ferraris P., Lee J. and Lifschitz V. 2007. A new perspective on stable models. In Proc. of the 20th International Joint Conference on Artificial Intelligence (IJCAI'07). Sangal R., Mehta H. and Bagga R. K., Eds. Morgan, Kaufmann Publishers Inc., San Francisco, CA, USA, 372379.
Gebser M., Kaminski R., Kaufmann B., Ostrowski M., Schaub T. and Thiele S. 2008. Engineering an incremental ASP solver. In Proc. of the 24th International Conference on Logic Programming (ICLP'08), de la Banda M. Garcia and Pontelli E., Eds. LNCS, vol. 5366. Springer, 190205.
Gebser M., Kaminski R., König A. and Schaub T. 2011. Advances in gringo Series 3. In Proc. of 11th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'11), Delgrande J. P. and Faber W., Eds. LNCS, vol. 6645. Springer, 345351.
Gebser M., Kaufmann B. and Schaub T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187, 5289.
Gebser M., Schaub T. and Thiele S. 2007. GrinGo: A new grounder for answer set programming. In Proc. of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'07). LNCS, vol. 4483. Springer, 266271.
Gelfond M. and Lifschitz V. 1988. The stable model semantics for logic programming. In Proc. of the 5th International Conference and Symposium on Logic Programming (ICLP'88), Kowalski R. A. and Bowen K., Eds. The MIT Press, Cambridge, Massachusetts, 10701080.
Gelfond M. and Lifschitz V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9 (3/4), 365386.
Giunchiglia E., Lierler Y. and Maratea M. 2006. Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36 (4), 345377.
Gottlob G., Marcus S., Nerode A., Salzer G. and Subrahmanian V. S. 1996. A non-ground realization of the stable and well-founded semantics. Theoretical Computer Science 166 (1–2), 221262.
Greco S., Molinaro C. and Trubitsyna I. 2013. Logic programming with function symbols: Checking termination of bottom-up evaluation through program adornments. Theory and Practice of Logic Programming 13 (4–5), 737752.
Konczak K., Linke T. and Schaub T. 2006. Graphs and colorings for answer set programming. Theory and Practice of Logic Programming 6, 61106.
Lefèvre C. and Nicolas P. 2009a. A first order forward chaining approach for answer set computing. In Proc. of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'09), Erdem Esra, Lin Fangzhen and Schaub Torsten, Eds. LNCS, vol. 5753. Springer, 196208.
Lefèvre C. and Nicolas P. 2009b. The first version of a new ASP solver: ASPeRiX . In Proc. of the 12th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'09), Erdem Esra, Lin Fangzhen and Schaub Torsten, Eds. LNCS, vol. 5753. Springer, 522527.
Leone N., Pfeifer G., Faber W., Eiter T., Gottlob G., Perri S. and Scarcello F. 2006. The DLV system for knowledge representation and reasoning. ACM Transactions on Computational Logic 7 (3), 499562.
Lierler Y. and Lifschitz V. 2009. One more decidable class of finitely ground programs. In Proc. of the 25th International Conference on Logic Programming (ICLP'09), Hill P. M. and Warren D. S., Eds. LNCS, vol. 5649. Springer, 489493.
Lin F. and Zhao Y. 2004. ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157 (1–2), 115137.
Lin F. and Zhou Y. 2007. From answer set logic programming to circumscription via logic of GK. In Proc. of the 20th International Joint Conference on Artificial Intelligence (IJCAI'07), Sangal R., Mehta H. and Bagga R. K., Eds. Morgan, Kaufmann Publishers Inc., San Francisco, CA, USA, 441446.
Liu L., Pontelli E., Son T. C. and Truszczynski M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artificial Intelligence 174 (3–4), 295315.
Liu L. and Truszczynski M. 2005. Pbmodels - software to compute stable models by pseudoboolean solvers. In Proc. of the 8th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05), Baral C., Greco G., Leone N., and Terracina G., Eds. LNCS, vol. 3662. Springer, 410415.
Niemelä I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25 (3–4), 241273.
Ostrowski M. and Schaub T. 2012. ASP modulo CSP: The clingcon system. Theory and Practice of Logic Programming 12 (4–5), 485503.
Perri S., Scarcello F., Catalano G. and Leone N. 2007. Enhancing dlv instantiator by backjumping techniques. Annals of Mathematics and Artificial Intelligence 51 (2–4), 195228.
Simons P., Niemelä I. and Soininen T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138 (1–2), 181234.
Syrjänen T. 1998. Implementation of Local Grounding for Logic Programs for Stable Model semantics. Technical Report, Helsinki University of Technology.
Truszczynski M. 2012. Connecting first-order ASP and the logic FO(ID) through reducts. In Correct Reasoning - Essays on Logic-Based AI in Honour of Vladimir Lifschitz, Erdem E., Lee J., Lierler Y. and Pearce D., Eds. LNCS, vol. 7265. Springer, 543559.
Ullman J. D. 1989. Principles of Database and Knowledge-Base Systems, Volume II. Computer Science Press.
Weinzierl A. 2013. Learning non-ground rules for answer-set solving. In Proc. 2nd Workshop on Grounding and Transformations for Theories With Variables (GTTV'13).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
  • URL: /core/journals/theory-and-practice-of-logic-programming
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Type Description Title
PDF
Supplementary Materials

Lefevre supplementary material
Lefevre supplementary material 1

 PDF (194 KB)
194 KB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 31 *
Loading metrics...

Abstract views

Total abstract views: 238 *
Loading metrics...

* Views captured on Cambridge Core between 16th January 2017 - 22nd November 2017. This data will be updated every 24 hours.