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Vicious Circle Principle and Logic Programs with Aggregates

Published online by Cambridge University Press:  21 July 2014

MICHAEL GELFOND  and
YUANLIN ZHANG
MICHAEL GELFOND
Affiliation:
Texas Tech University, Lubbock, Texas 79414, USA (email: michael.gelfond@ttu.edu, y.zhang@ttu.edu)
YUANLIN ZHANG
Affiliation:
Texas Tech University, Lubbock, Texas 79414, USA (email: michael.gelfond@ttu.edu, y.zhang@ttu.edu)
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Abstract

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.

Keywords

AggregatesAnswer Set Programming
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 14 , Special Issue 4-5: 30th International Conference on Logic Programming , July 2014 , pp. 587 - 601
Copyright
Copyright © Cambridge University Press 2014 

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References

Balai, E., Gelfond, M., and Zhang, Y. 2013. Towards answer set programming with sorts. In LPNMR. 135–147.CrossRefGoogle Scholar
Brewka, G., Eiter, T., and Truszczynski, M. 2011. Answer set programming at a glance. Commun. ACM 54, 12, 92–103.CrossRefGoogle Scholar
Erdem, E., Lee, J., and Lierler, Y. 2012. Theory and practice of answer set programming. AAAI-2012 Tutorial (http://peace.eas.asu.edu/aaai12tutorial/asp-tutorial-aaai.pdf).Google Scholar
Faber, W., Pfeifer, G., and Leone, N. 2011. Semantics and complexity of recursive aggregates in answer set programming. Artificial Intelligence 175, 1, 278–298.CrossRefGoogle Scholar
Faber, W., Pfeifer, G., Leone, N., Dell'Armi, T., and Ielpa, G. 2008. Design and implementation of aggregate functions in the dlv system. TPLP 8, 5-6, 545–580.Google Scholar
Feferman, S. 2002. Predicativity. http://math.stanford.edu/~feferman/papers/ Google Scholar
Ferraris, P. 2005. Answer sets for propositional theories. In LPNMR. 119–131.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B., and Schaub, T. 2009. On the implementation of weight constraint rules in conflict-driven asp solvers. In ICLP. 250–264.CrossRefGoogle Scholar
Gebser, M., Kaufman, B., Neumann, A., and Schaub, T. 2007. Conflict-driven answer set enumeration. In Proceedings of the 9th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'07), Baral, C., Brewka, G., and Schlipf, J., Eds. lnai, vol. 3662. Springer, 136–148.CrossRefGoogle Scholar
Gelfond, M. 2002. Representing Knowledge in A-Prolog. In Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II, Kakas, A. C. and Sadri, F., Eds. Vol. 2408. Springer Verlag, Berlin, 413–451.CrossRefGoogle Scholar
Gelfond, M. and Kahl, Y. 2014. Knowledge Representation, Reasoning, and the Design of Intelligent Agents. Cambridge University Press.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proceedings of ICLP-88. 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.CrossRefGoogle Scholar
Harrison, A., Lifschitz, V., and Yang, F. 2013. On the semantics of gringo. In Working Notes of the Workshop on Answer Set Programming and Other Computing Paradigms.Google Scholar
Kemp, D. B. and Stuckey, P. J. 1991. Semantics of logic programs with aggregates. In ISLP. Vol. 91. Citeseer, 387–401.Google Scholar
Koch, C., Leone, N., and Pfeifer, G. 2003. Enhancing disjunctive logic programming systems by sat checkers. Artif. Intell. 151, 1-2, 177–212.CrossRefGoogle 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, 499–562.CrossRefGoogle Scholar
Liu, L., Pontelli, E., Son, T. C., and Truszczynski, M. 2010. Logic programs with abstract constraint atoms: The role of computations. Artif. Intell. 174, 3-4, 295–315.CrossRefGoogle Scholar
Marek, V. W., Truszczynski, M., et al. 2004. Logic programs with abstract constraint atoms. In AAAI. Vol. 4. 86–91.Google Scholar
Niemela, I., Simons, P., and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2 (Jun), 181–234.Google Scholar
Pelov, N., Denecker, M., and Bruynooghe, M. 2007. Well-fouded and stable semantics of logic programs with aggregates. Theory and Practice of Logic Programming 7, 355–375.CrossRefGoogle Scholar
Poincare, H. 1906. Les mathematiques et la logique. Review de metaphysique et de morale 14, 294–317.Google Scholar
Son, T. C. and Pontelli, E. 2007. A constructive semantic characterization of aggregates in answer set programming. TPLP 7, 3, 355–375.Google Scholar
Wang, Y., Lin, F., Zhang, M., and You, J.-H. 2012. A well-founded semantics for basic logic programs with arbitrary abstract constraint atoms. In AAAI.Google Scholar
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Vicious Circle Principle and Logic Programs with Aggregates

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