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FOLASP: FO(·) as Input Language for Answer Set Solvers

Published online by Cambridge University Press:  19 November 2021

KYLIAN VAN DESSEL Open the ORCID record for KYLIAN VAN DESSEL [Opens in a new window] ,
JO DEVRIENDT  and
JOOST VENNEKENS
KYLIAN VAN DESSEL
Affiliation:
KU Leuven, Dept. of Computer Science, De Nayer Campus, Sint-Katelijne-Waver, Belgium Leuven.AI – KU Leuven Institute for AI, Leuven, Belgium (e-mails: [email protected], [email protected], [email protected])
JO DEVRIENDT
Affiliation:
KU Leuven, Dept. of Computer Science, De Nayer Campus, Sint-Katelijne-Waver, Belgium Leuven.AI – KU Leuven Institute for AI, Leuven, Belgium (e-mails: [email protected], [email protected], [email protected])
JOOST VENNEKENS
Affiliation:
KU Leuven, Dept. of Computer Science, De Nayer Campus, Sint-Katelijne-Waver, Belgium Leuven.AI – KU Leuven Institute for AI, Leuven, Belgium (e-mails: [email protected], [email protected], [email protected])
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Abstract

Technological progress in Answer Set Programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(·), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(·). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(·) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(·) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(·).

Keywords

declarative programmingfirst order logicanswer set programming
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 21 , Special Issue 6: 37th International Conference on Logic Programming Special Issue II , November 2021 , pp. 785 - 801
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Aavani, A. 2014. Enfragmo: A System for Grounding Extended First-Order Logic to SAT. Ph.D. thesis, Faculty of Applied Sciences, Simon Fraser University, Vancouver, Canada.Google Scholar
Alviano, M., Calimeri, F., Charwat, G., Dao-Tran, M., Dodaro, C., Ianni, G., Krennwallner, T., Kronegger, M., Oetsch, J., Pfandler, A., Pührer, J., Redl, C., Ricca, F., Schneider, P., Schwengerer, M., Spendier, L. K., Wallner, J. P. and Xiao, G. 2013. The fourth Answer Set Programming competition: Preliminary report. In Logic Programming and Nonmonotonic Reasoning, 12th International Conference, LPNMR 2013, Corunna, Spain, September 15-19, 2013. Proceedings, Cabalar, P. and Son, T. C., Eds. LNCS, vol. 8148. Springer, 42–53.Google Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Maratea, M., Ricca, F. and Schaub, T. 2020. ASP-Core-2 input language format. TPLP 20, 2, 294–309.Google Scholar
Calimeri, F., Gebser, M., Maratea, M. and Ricca, F. 2016. Design and results of the fifth answer set programming competition. Artificial Intelligence 231, 151–181.10.1016/j.artint.2015.09.008CrossRefGoogle Scholar
De Cat, B., Bogaerts, B., Bruynooghe, M., Janssens, G. and Denecker, M. 2016. Predicate logic as a modelling language: The IDP system. CoRR abs/1401.6312v2. Google Scholar
De Cat, B., Bogaerts, B., Devriendt, J. and Denecker, M. 2013. Model expansion in the presence of function symbols using constraint programming. In ICTAI. IEEE, 1068–1075.Google Scholar
De Cat, B., Denecker, M., Bruynooghe, M. and Stuckey, P. J. 2015. Lazy model expansion: Interleaving grounding with search. Journal of Artificial Intelligence Research (JAIR) 52, 235–286.10.1613/jair.4591CrossRefGoogle Scholar
Denecker, M., Lierler, Y., Truszczynsky, M. and Vennekens, J. 2012. A Tarskian informal semantics for answer set programming. In Technical Communications of the 28th International Conference on Logic Programming. Vol. 17. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 227–289.Google Scholar
Denecker, M. and Ternovska, E. 2008. A logic of nonmonotone inductive definitions. ACM Transactions on Computational Logic 9, 2(April), 14:1–14:52.10.1145/1342991.1342998CrossRefGoogle Scholar
Enderton, H. B. 2001. Chapter two - first-order logic. In A Mathematical Introduction to Logic (Second Edition), 2nd ed., H. B. Enderton, Ed. Press, Academic, Boston, 67–181.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T. and Wanko, P. 2016. Theory solving made easy with Clingo 5. In Technical Communications of the 32nd International Conference on Logic Programming, ICLP 2016 TCs, October 16–21, 2016, New York City, USA, Carro, M., King, A., De Vos, M., and Saeedloei, N., Eds. OASIcs, vol. 52. Schloss Dagstuhl, 2:1–2:15.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2019. Multi-shot ASP solving with clingo. Theory and Practice of Logic Programming 19, 1, 27–82.Google Scholar
Gebser, M., Maratea, M. and Ricca, F. 2020. The seventh answer set programming competition: Design and results. Theory and Practice of Logic Programming 20, 2, 176–204.10.1017/S1471068419000061CrossRefGoogle 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, 499–562.10.1145/1149114.1149117CrossRefGoogle Scholar
Marek, V. and Truszczyński, M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective, Apt, K. R., Marek, V., Truszczyński, M., and Warren, D. S., Eds. Springer-Verlag, 375–398.10.1007/978-3-642-60085-2_17CrossRefGoogle Scholar
Mariën, M., Gilis, D. and Denecker, M. 2004. On the relation between ID-Logic and answer set programming. In JELIA, Alferes, J. J. and Leite, J. A., Eds. LNCS, vol. 3229. Springer, 108–120.Google Scholar
Van Gelder, A., Ross, K. A. and Schlipf, J. S. 1988. Unfounded sets and well-founded semantics for general logic programs. In PODS. ACM, 221–230.Google Scholar
Van Gelder, A., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of ACM 38, 3 (July), 619–649.10.1145/116825.116838CrossRefGoogle Scholar