Hostname: page-component-89b8bd64d-z2ts4 Total loading time: 0 Render date: 2026-05-07T11:22:45.702Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  16 January 2017

CLAIRE LEFÈVRE ,
CHRISTOPHER BÉATRIX ,
IGOR STÉPHAN  and
LAURENT GARCIA
CLAIRE LEFÈVRE
Affiliation:
LERIA, University of Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France (e-mails: claire@info.univ-angers.fr, beatrix@info.univ-angers.fr, stephan@info.univ-angers.fr, garcia@info.univ-angers.fr)
CHRISTOPHER BÉATRIX
Affiliation:
LERIA, University of Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France (e-mails: claire@info.univ-angers.fr, beatrix@info.univ-angers.fr, stephan@info.univ-angers.fr, garcia@info.univ-angers.fr)
IGOR STÉPHAN
Affiliation:
LERIA, University of Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France (e-mails: claire@info.univ-angers.fr, beatrix@info.univ-angers.fr, stephan@info.univ-angers.fr, garcia@info.univ-angers.fr)
LAURENT GARCIA
Affiliation:
LERIA, University of Angers, 2 Boulevard Lavoisier, 49045 Angers Cedex 01, France (e-mails: claire@info.univ-angers.fr, beatrix@info.univ-angers.fr, stephan@info.univ-angers.fr, garcia@info.univ-angers.fr)
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Answer set programmingsolver implementationgrounding on the flyfirst-orderforward chaining

Information

Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Issue 3 , May 2017 , pp. 266 - 310
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

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

References

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, 1–24.Google Scholar
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, 55–67.Google Scholar
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), 497–512.CrossRefGoogle Scholar
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.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.CrossRefGoogle Scholar
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, 52–66.Google Scholar
Baselice, S. and Bonatti, P. A. 2010. A decidable subclass of finitary programs. Theory and Practice of Logic Programming 10 (4–6), 481–496.CrossRefGoogle Scholar
Buccafurri, F., Leone, N. and Rullo, P. 2000. Enhancing disjunctive datalog by constraints. IEEE Transactions on Knowledge and Data Engineering 12 (5), 845–860.Google Scholar
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, 407–424.Google Scholar
Calimeri, F., Cozza, S., Ianni, G. and Leone, N. 2011. Finitely recursive programs: Decidability and bottom-up computation. AI Communications 24 (4), 311–334.CrossRefGoogle Scholar
Calimeri, F., Ianni, G. and Ricca, F. 2014. The third open answer set programming competition. Theory and Practice of Logic Programming 14 (1), 117–135.Google Scholar
Calimeri, F., Perri, S. and Ricca, F. 2008. Experimenting with parallelism for the instantiation of ASP programs. Journal of Algorithms 63 (1–3), 34–54.CrossRefGoogle Scholar
Dal Palù, A., Dovier, A., Pontelli, E. and Rossi, G. 2009. Gasp: Answer set programming with lazy grounding. Fundamenta Informaticae 96 (3), 297–322.Google Scholar
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, 480–483.CrossRefGoogle Scholar
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, 198–217.Google Scholar
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, 247–264.Google Scholar
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, 177–191.CrossRefGoogle Scholar
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, 372–379.Google Scholar
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, 190–205.Google Scholar
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, 345–351.Google Scholar
Gebser, M., Kaufmann, B. and Schaub, T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187, 52–89.Google Scholar
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, 266–271.Google Scholar
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, 1070–1080.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9 (3/4), 365–386.Google Scholar
Giunchiglia, E., Lierler, Y. and Maratea, M. 2006. Answer set programming based on propositional satisfiability. Journal of Automated Reasoning 36 (4), 345–377.Google Scholar
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), 221–262.Google Scholar
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), 737–752.Google Scholar
Konczak, K., Linke, T. and Schaub, T. 2006. Graphs and colorings for answer set programming. Theory and Practice of Logic Programming 6, 61–106.Google Scholar
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, 196–208.CrossRefGoogle Scholar
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, 522–527.Google Scholar
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), 499–562.Google Scholar
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, 489–493.Google Scholar
Lin, F. and Zhao, Y. 2004. ASSAT: Computing answer sets of a logic program by SAT solvers. Artificial Intelligence 157 (1–2), 115–137.Google Scholar
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, 441–446.Google Scholar
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), 295–315.Google Scholar
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, 410–415.Google Scholar
Niemelä, I. 1999. Logic programs with stable model semantics as a constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25 (3–4), 241–273.Google Scholar
Ostrowski, M. and Schaub, T. 2012. ASP modulo CSP: The clingcon system. Theory and Practice of Logic Programming 12 (4–5), 485–503.Google Scholar
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), 195–228.CrossRefGoogle Scholar
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138 (1–2), 181–234.Google Scholar
Syrjänen, T. 1998. Implementation of Local Grounding for Logic Programs for Stable Model semantics. Technical Report, Helsinki University of Technology.Google Scholar
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, 543–559.Google Scholar
Ullman, J. D. 1989. Principles of Database and Knowledge-Base Systems, Volume II. Computer Science Press.Google Scholar
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).Google Scholar
Supplementary material: PDF

Lefevre supplementary material

Lefevre supplementary material 1

Download Lefevre supplementary material(PDF)
PDF 193.8 KB