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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
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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BanbaraM., GebserM., InoueK., OstrowskiM., PeanoA., SchaubT., SohT., TamuraN. and WeiseM. 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.
BanbaraM., KaufmannB., OstrowskiM. and SchaubT. 2017. Clingcon: The next generation. Theory and Practice of Logic Programming 17, 4, 408461.
BaralC. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.
BarrettC., SebastianiR., SeshiaS. and TinelliC. 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.
BartholomewM. and LeeJ. 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.
CabalarP., OteroR. and PoseS. 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.
CarroM. and KingA., Eds. 2016. Technical Communications of the 32nd International Conference on Logic Programming (ICLP'16). vol. 52. Open Access Series in Informatics (OASIcs).
CottonS. and MalerO. 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.
CrawfordJ. and BakerA. 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.
DantzigG. 1963. Linear Programming and Extensions. Princeton University Press.
De RosisA., EiterT., RedlC. and RiccaF. 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.
DrescherC. and WalshT. 2010. A translational approach to constraint answer set solving. Theory and Practice of Logic Programming 10, 4–6, 465480.
GebserM., KaminskiR., KaufmannB., OstrowskiM., SchaubT. and WankoP. 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.
GebserM., KaminskiR., KaufmannB. and SchaubT. 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.
GebserM., KaufmannB. and SchaubT. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187–188, 5289.
GelfondM. and LifschitzV. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365385.
GoldbergD. 1991. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys (CSUR) 23, 1, 548.
JanhunenT., LiuG. and NiemeläI. 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.
LierlerY. and SusmanB. 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.
LiuG., JanhunenT. and NiemeläI. 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.
SimonsP., NiemeläI. and SoininenT. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181234.
SohT., InoueK., TamuraN., BanbaraM. and NabeshimaH. 2010. A SAT-based method for solving the two-dimensional strip packing problem. Fundamenta Informaticae 102, 3–4, 467487.
TaillardE. 1993. Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 2, 278285.
van LoonJ. 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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