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Clingo goes linear constraints over reals and integers*

  • TOMI JANHUNEN (a1), ROLAND KAMINSKI (a2), MAX OSTROWSKI (a2), SEBASTIAN SCHELLHORN (a2), PHILIPP WANKO (a2) and TORSTEN SCHAUB (a3)...
Abstract

The recent series 5 of the Answer Set Programming (ASP) system clingo provides generic means to enhance basic ASP with theory reasoning capabilities. We instantiate this framework with different forms of linear constraints and elaborate upon its formal properties. Given this, we discuss the respective implementations, and present techniques for using these constraints in a reactive context. More precisely, we introduce extensions to clingo with difference and linear constraints over integers and reals, respectively, and realize them in complementary ways. Finally, we empirically evaluate the resulting clingo derivatives clingo[dl] and clingo[lp] on common language fragments and contrast them to related ASP systems.

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Banbara, M., Gebser, M., Inoue, K., Ostrowski, M., Peano, A., Schaub, T., Soh, T., Tamura, N. and Weise, M. 2015. Aspartame: Solving constraint satisfaction problems with answer set programming. In Proc. of the 13th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'15), Calimeri, F., Ianni, G. and Truszczyński, M., Eds. Lecture Notes in Artificial Intelligence, vol. 9345. Springer-Verlag, 112–126.
Banbara, M., Kaufmann, B., Ostrowski, M. and Schaub, T. 2017. Clingcon: The next generation. Theory and Practice of Logic Programming 17, 4, 408461.
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.
Barrett, C., Sebastiani, R., Seshia, S. and Tinelli, C. 2009. Satisfiability modulo theories. In Handbook of Satisfiability, vol. 185, Biere, A., Heule, M., van Maaren, H. and Walsh, T., Eds. Frontiers in Artificial Intelligence and Applications. IOS Press, Chapter 26, 825885.
Bartholomew, M. and Lee, J. 2014. System aspmt2smt: Computing ASPMT theories by SMT solvers. In Proc. of the 14th European Conference on Logics in Artificial Intelligence (JELIA'14), Fermé, E. and Leite, J., Eds. Lecture Notes in Artificial Intelligence, vol. 8761. Springer-Verlag, 529–542.
Cabalar, P., Otero, R. and Pose, S. 2000. Temporal constraint networks in action. In Proc. of the 14th European Conference on Artificial Intelligence (ECAI'00), Horn, W., Ed. IOS Press, 543–547.
Carro, M. and King, A., Eds. 2016. Technical Communications of the 32nd International Conference on Logic Programming (ICLP'16). vol. 52. Open Access Series in Informatics (OASIcs).
Cotton, S. and Maler, O. 2006. Fast and flexible difference constraint propagation for DPLL (T). In Proc. of the 9th International Conference on Theory and Applications of Satisfiability Testing (SAT'06), Biere, A. and Gomes, C., Eds. Lecture Notes in Computer Science, vol. 4121. Springer-Verlag, 170–183.
Crawford, J. and Baker, A. 1994. Experimental results on the application of satisfiability algorithms to scheduling problems. In Proc. of the 12th National Conference on Artificial Intelligence (AAAI'94), Hayes-Roth, B. and Korf, R., Eds. AAAI Press, 1092–1097.
Dantzig, G. 1963. Linear Programming and Extensions. Princeton University Press.
De Rosis, A., Eiter, T., Redl, C. and Ricca, F. 2015. Constraint answer set programming based on HEX-programs. In Proc. of the 8th Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP'15), Inclezan, D. and Maratea, M., Eds.
Drescher, C. and Walsh, T. 2010. A translational approach to constraint answer set solving. Theory and Practice of Logic Programming 10, 4–6, 465480.
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T. and Wanko, P. 2016. Theory solving made easy with clingo 5. Technical Communications of the 32nd International Conference on Logic Programming (ICLP'16). vol. 52. Open Access Series in Informatics (OASIcs), 2:1–2:15.
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo = ASP + control: Preliminary report. In Technical Communications of the 30th International Conference on Logic Programming (ICLP'14), Leuschel, M. and Schrijvers, T., Eds. Theory and Practice of Logic Programming, Online Supplement, vol. arXiv:1405.3694v1. Available at http://arxiv.org/abs/1405.3694v1.
Gebser, M., Kaufmann, B. and Schaub, T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187–188, 5289.
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365385.
Goldberg, D. 1991. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys (CSUR) 23, 1, 548.
Janhunen, T., Liu, G. and Niemelä, I. 2011. Tight integration of non-ground answer set programming and satisfiability modulo theories. In Proc. of the 1st Workshop on Grounding and Transformation for Theories with Variables (GTTV'11), Cabalar, P., Mitchell, D., Pearce, D. and Ternovska, E., Eds. 1–13.
Lierler, Y. and Susman, B. 2016. SMT-based constraint answer set solver EZSMT (system description). Technical Communications of the 32nd International Conference on Logic Programming (ICLP'16). vol. 52. Open Access Series in Informatics (OASIcs), 1:1–1:15.
Liu, G., Janhunen, T. and Niemelä, I. 2012. Answer set programming via mixed integer programming. In Proc. of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR'12), Brewka, G., Eiter, T. and McIlraith, S., Eds. AAAI Press, 32–42.
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181234.
Soh, T., Inoue, K., Tamura, N., Banbara, M. and Nabeshima, H. 2010. A SAT-based method for solving the two-dimensional strip packing problem. Fundamenta Informaticae 102, 3–4, 467487.
Taillard, E. 1993. Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 2, 278285.
van Loon, J. 1981. Irreducibly inconsistent systems of linear inequalities. European Journal of Operational Research 3, 283288.
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Theory and Practice of Logic Programming
  • ISSN: 1471-0684
  • EISSN: 1475-3081
  • URL: /core/journals/theory-and-practice-of-logic-programming
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