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Here and There with Arithmetic

Published online by Cambridge University Press:  23 September 2021

VLADIMIR LIFSCHITZ Open the ORCID record for VLADIMIR LIFSCHITZ [Opens in a new window]
VLADIMIR LIFSCHITZ*
Affiliation:
University of Texas at Austin, USA
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In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Keywords

answer set programmingstable modelsstrong equivalence
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. 735 - 749
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Fandinno, J., Lifschitz, V., Lühne, P. and Schaub, T. 2020. Verifying tight programs with Anthem and Vampire. Theory and Practice of Logic Programming 20.10.1017/S1471068420000344CrossRefGoogle Scholar
Gebser, M., Harrison, A., Kaminski, R., Lifschitz, V. and Schaub, T. 2015. Abstract Gringo. Theory and Practice of Logic Programming 15, 449–463.10.1017/S1471068415000150CrossRefGoogle Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Lindauer, M., Ostrowski, M., Romero, J., Schaub, T. and Thiele, S. 2019. Potassco User Guide. Available at https://github.com/potassco/guide/releases/ Google Scholar
Harrison, A., Lifschitz, V., Pearce, D. and Valverde, A. 2017. Infinitary equilibrium logic and strongly equivalent logic programs. Artificial Intelligence 246, 22–33.10.1016/j.artint.2017.02.002CrossRefGoogle Scholar
Heyting, A. 1930. Die formalen Regeln der intuitionistischen Logik. Sitzungsberichte der Preussischen Akademie von Wissenschaften. Physikalisch-mathematische Klasse, 42–56.Google Scholar
Hosoi, T. 1966. The axiomatization of the intermediate propositional systems S n of Gödel. Journal of the Faculty of Science of the University of Tokyo 13, 183–187.Google Scholar
Lifschitz, V. 2021. Transforming gringo rules into formulas in a natural way. In Proceedings of European Conference on Artificial Intelligence.10.1007/978-3-030-75775-5_28CrossRefGoogle Scholar
Lifschitz, V., Lühne, P. and Schaub, T. 2019. Verifying strong equivalence of programs in the input language of gringo. In Proceedings of the 15th International Conference on Logic Programming and Non-monotonic Reasoning.10.1007/978-3-030-20528-7_20CrossRefGoogle Scholar
Lifschitz, V., Lühne, P. and Schaub, T. 2020. Towards verifying logic programs in the input language of clingo. In Fields of Logic and Computation III, Essays Dedicated to Yuri Gurevich on the Occasion of His 80th Birthday. Springer, 190–209.Google Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2001. Strongly equivalent logic programs. ACM Transactions on Computational Logic 2, 526–541.10.1145/383779.383783CrossRefGoogle Scholar
Lifschitz, V., Pearce, D. and Valverde, A. 2007. A characterization of strong equivalence for logic programs with variables. In Proceedings of International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR), 188–200.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 Honor of Vladimir Lifschitz, Erdem, E., Lee, J., Lierler, Y., and Pearce, D., Eds. Springer, 543–559.10.1007/978-3-642-30743-0_37CrossRefGoogle Scholar