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Better Paracoherent Answer Sets with Less Resources

Published online by Cambridge University Press:  20 September 2019

GIOVANNI AMENDOLA Open the ORCID record for GIOVANNI AMENDOLA [Opens in a new window] ,
CARMINE DODARO Open the ORCID record for CARMINE DODARO [Opens in a new window]  and
FRANCESCO RICCA Open the ORCID record for FRANCESCO RICCA [Opens in a new window]
GIOVANNI AMENDOLA
Affiliation:
University of Calabria, Rende, Italy (e-mails: amendola@mat.unical.it, dodaro@mat.unical.it, ricca@mat.unical.it)
CARMINE DODARO
Affiliation:
University of Calabria, Rende, Italy (e-mails: amendola@mat.unical.it, dodaro@mat.unical.it, ricca@mat.unical.it)
FRANCESCO RICCA
Affiliation:
University of Calabria, Rende, Italy (e-mails: amendola@mat.unical.it, dodaro@mat.unical.it, ricca@mat.unical.it)
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Abstract

Answer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP programs can be considered as a modeling feature, it turns out to be a weakness in many other cases, and especially for query answering. Paracoherent answer set semantics extend the classical semantics of ASP to draw meaningful conclusions also from incoherent programs, with the result of increasing the range of applications of ASP. State of the art implementations of paracoherent ASP adopt the semi-equilibrium semantics, but cannot be lifted straightforwardly to compute efficiently the (better) split semi-equilibrium semantics that discards undesirable semi-equilibrium models. In this paper an efficient evaluation technique for computing a split semi-equilibrium model is presented. An experiment on hard benchmarks shows that better paracoherent answer sets can be computed consuming less computational resources than existing methods.

Keywords

Answer Set ProgrammingParacoherent reasoningSemi-equilibrium models
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 19 , Special Issue 5-6: 35th International Conference on Logic Programming , September 2019 , pp. 757 - 772
Copyright
© Cambridge University Press 2019 

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References

Alcântara, J., Damásio, C. V., and Pereira, L. M. 2005. An encompassing framework for paraconsistent logic programs. Journal of Applied Logic 3, 1, 67–95.CrossRefGoogle Scholar
Alviano, M. 2018. Query answering in propositional circumscription. In Proceedings of the International Conference on Artificial Intelligence (IJCAI). ijcai.org, 1669–1675.Google Scholar
Alviano, M., Amendola, G., Dodaro, C., Leone, N., Maratea, M., and Ricca, F. 2019. Evaluation of disjunctive programs in WASP. In Proceedings of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). Lecture Notes in Computer Science, vol. 11481. Springer, 241–255.CrossRefGoogle Scholar
Alviano, M., Calimeri, F., Dodaro, C., Fuscà, D., Leone, N., Perri, S., Ricca, F., Veltri, P., and Zangari, J. 2017. The ASP system DLV2. In Proceedings of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). Lecture Notes in Computer Science, vol. 10377. Springer, 215–221.CrossRefGoogle Scholar
Alviano, M. and Dodaro, C. 2016. Anytime answer set optimization via unsatisfiable core shrinking. Theory and Practice of Logic Programming 16, 5-6, 533–551.Google Scholar
Alviano, M., Dodaro, C., Leone, N., and Ricca, F. 2015. Advances in WASP. In Proceedings of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). Lecture Notes in Computer Science. 40–54.Google Scholar
Amendola, G., Dodaro, C., Faber, W., Leone, N., and Ricca, F. 2017. On the computation of paracoherent answer sets. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI). 1034–1040.Google Scholar
Amendola, G., Dodaro, C., Faber, W., and Ricca, F. 2018. Externally supported models for efficient computation of paracoherent answer sets. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI). AAAI Press, 1720–1727.Google Scholar
Amendola, G., Eiter, T., Fink, M., Leone, N., and Moura, J. 2016. Semi-equilibrium models for paracoherent answer set programs. Artificial Intelligence 234, 219–271.Google Scholar
Angiulli, F., Ben-Eliyahu, R., Fassetti, F., and Palopoli, L. 2014. On the tractability of minimal model computation for some CNF theories. Artificial Intelligence 210, 56–77.Google Scholar
Arenas, M., Bertossi, L. E., and Chomicki, J. 2003. Answer sets for consistent query answering in inconsistent databases. Theory and Practice of Logic Programming 3, 4-5, 393–424.Google Scholar
Balduccini, M. and Gelfond, M. 2003. Logic programs with consistency-restoring rules. In Proceedings of the International Symposium on Logical Formalization of Commonsense Reasoning, AAAI Spring Symposium Series. Vol. 102. 9–18.Google Scholar
Balduccini, M., Gelfond, M., Watson, R., and Nogueira, M. 2001. The usa-advisor: A case study in answer set planning. In Proceedings of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). Lecture Notes in Computer Science, vol. 2173. Springer, 439–442.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning, and Declarative Problem Solving. Cambridge University Press, New York, NY, USA.CrossRefGoogle Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Communications of the ACM 54, 12, 92–103.Google Scholar
Bry, F. and Yahya, A. H. 2000. Positive unit hyperresolution tableaux and their application to minimal model generation. Journal of Automated Reasoning 25, 1, 35–82.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., Gebser, M., Maratea, M., and Ricca, F. 2016. Design and results of the fifth answer set programming competition. Artificial Intelligence 231, 151–181.Google Scholar
Campeotto, F., Dovier, A., and Pontelli, E. 2015. A declarative concurrent system for protein structure prediction on GPU. Journal of Experimental & Theoretical Artificial Intelligence 27, 5, 503–541.CrossRefGoogle Scholar
Costantini, S. and Formisano, A. 2016. Query answering in resource-based answer set semantics. Theory and Practice of Logic Programming 16, 5-6, 619–635.Google Scholar
Cuteri, B., Dodaro, C., and Ricca, F. 2019. Debugging of answer set programs using paracoherent reasoning. In Proceedings of the Italian Conference on Computational Logic (CILC). CEUR Workshop Proceedings, vol. 2396. CEUR-WS.org, 289–299.Google Scholar
Dodaro, C., Gasteiger, P., Leone, N., Musitsch, B., Ricca, F., and Shchekotykhin, K. 2016. Combining Answer Set Programming and domain heuristics for solving hard industrial problems (Application Paper). Theory and Practice of Logic Programming 16, 5-6, 653–669.Google Scholar
Dodaro, C., Leone, N., Nardi, B., and Ricca, F. 2015. Allotment problem in travel industry: A solution based on ASP. In Proceedings of the International Conference on Web Reasoning and Rule Systems (RR). Lecture Notes in Computer Science, vol. 9209. Springer, 77–92.Google Scholar
Eiter, T., Fink, M., and Moura, J. 2010. Paracoherent answer set programming. In Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR).Google Scholar
Eiter, T., Ianni, G., and Krennwallner, T. 2009. Answer set programming: A primer. In Proceedings of the Reasoning Web International Summer School. Lecture Notes in Computer Science, vol. 5689. Springer, 40–110.Google Scholar
Eiter, T., Leone, N., and Saccà, D. 1997. On the partial semantics for disjunctive deductive databases. Annals of Mathematics and Artificial Intelligence 19, 1-2, 59–96.Google Scholar
Erdem, E., Gelfond, M., and Leone, N. 2016. Applications of answer set programming. AI Magazine 37, 3, 53–68.Google Scholar
Gaggl, S. A., Manthey, N., Ronca, A., Wallner, J. P., and Woltran, S. 2015. Improved answer-set programming encodings for abstract argumentation. Theory and Practice of Logic Programming 15, 4-5, 434–448.CrossRefGoogle Scholar
Galindo, M. J. O., Ramírez, J. R. A., and Carballido, J. L. 2008. Logical weak completions of paraconsistent logics. Journal of Logic and Computation 18, 6, 913–940.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Romero, J., and Schaub, T. 2015. Progress in clasp series 3. In Proceedings of the International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR). Lecture Notes in Computer Science, vol. 9345. Springer, 368–383.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2012. Answer Set Solving in Practice. Morgan & Claypool Publishers.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. 2016. What’s hot in the answer set programming competition. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI). AAAI Press, 4327–4329.Google Scholar
Gebser, M., Maratea, M., and Ricca, F. 2017. The sixth answer set programming competition. Journal of Artificial Intelligence Research 60, 41–95.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
Janota, M. and Marques-Silva, J. 2016. On the query complexity of selecting minimal sets for monotone predicates. Artificial Intelligence 233, 73–83.Google Scholar
Kleinberg, J. M. and Tardos, É. 2006. Algorithm design. Addison-Wesley.Google Scholar
Koshimura, M., Nabeshima, H., Fujita, H., and Hasegawa, R. 2009. Minimal model generation with respect to an atom set. In Proceedings of the International Workshop on First-Order Theorem Proving (FTP). CEUR Workshop Proceedings, vol. 556. CEUR-WS.org, 49–59.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., Maratea, M., and Ricca, F. 2016. Systems, engineering environments, and competitions. AI Magazine 37, 3, 45–52.Google Scholar
Lifschitz, V. 1999. Answer set planning. In Proceedings of the International Conference on Logic Programming (ICLP). MIT Press, 23–37.Google Scholar
Lifschitz, V. and Turner, H. 1994. Splitting a logic program. In Proceedings of the International Conference on Logic Programming (ICLP). MIT Press, 23–37.Google Scholar
Niemelä, I. 1996. A tableau calculus for minimal model reasoning. In Proceedings of the International Workshop on Theorem Proving with Analytic Tableaux and Related Methods (TABLEAUX). 278–294.Google Scholar
Pearce, D. 2006. Equilibrium logic. Annals of Mathematics and Artificial Intelligence 47, 1-2, 3–41.CrossRefGoogle Scholar
Pereira, L. M. and Pinto, A. M. 2007. Approved models for normal logic programs. In Proceedings of the International Conference on Logic for Programming Artificial Intelligence and Reasoning (LPAR). Lecture Notes in Computer Science, vol. 4790. 454–468.Google Scholar
Przymusinski, T. C. 1991. Stable semantics for disjunctive programs. New Generation Computing 9, 3/4, 401–424.Google Scholar
Sakama, C. and Inoue, K. 1995. Paraconsistent stable semantics for extended disjunctive programs. Journal of Logic and Computation 5, 3, 265–285.Google Scholar
Seipel, D. 1997. Partial evidential stable models for disjunctive deductive databases. In Proceedings of the International Workshop on Logic Programming and Knowledge Representation (LPKR). Lecture Notes in Computer Science, vol. 1471. Springer, 66–84.Google Scholar
van Gelder, A., Ross, K. A., and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. Journal of the ACM 38, 3, 620–650.Google Scholar
van Harmelen, F., Lifschitz, V., and Porter, B. W., Eds. 2008. Handbook of Knowledge Representation. Foundations of Artificial Intelligence, vol. 3. Elsevier.Google Scholar
You, J. and Yuan, L. 1994. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences 49, 2, 334–361.Google Scholar