Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-23T12:03:54.135Z Has data issue: false hasContentIssue false
  • English
  • Français

Clingo goes linear constraints over reals and integers*

Published online by Cambridge University Press:  11 September 2017

TOMI JANHUNEN ,
ROLAND KAMINSKI ,
MAX OSTROWSKI ,
SEBASTIAN SCHELLHORN ,
PHILIPP WANKO  and
TORSTEN SCHAUB
TOMI JANHUNEN
Affiliation:
Aalto University, AaltoFinland (e-mail: [email protected])
ROLAND KAMINSKI
Affiliation:
University of Potsdam, PotsdamGermany (e-mails: [email protected], [email protected], [email protected], [email protected])
MAX OSTROWSKI
Affiliation:
University of Potsdam, PotsdamGermany (e-mails: [email protected], [email protected], [email protected], [email protected])
SEBASTIAN SCHELLHORN
Affiliation:
University of Potsdam, PotsdamGermany (e-mails: [email protected], [email protected], [email protected], [email protected])
PHILIPP WANKO
Affiliation:
University of Potsdam, PotsdamGermany (e-mails: [email protected], [email protected], [email protected], [email protected])
TORSTEN SCHAUB
Affiliation:
University of Potsdam, Potsdam Germany and INRIA Rennes, RennesFrance (e-mail: [email protected])
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Constraint Answer Set Programming (CASP)Answer Set Programming (ASP)Constraint Processing (CP)Theory Solving
Type
Regular Papers
Information
Theory and Practice of Logic Programming , Volume 17 , Special Issue 5-6: 33rd International Conference on Logic Programming , September 2017 , pp. 872 - 888
Copyright
Copyright © Cambridge University Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

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.Google Scholar
Banbara, M., Kaufmann, B., Ostrowski, M. and Schaub, T. 2017. Clingcon: The next generation. Theory and Practice of Logic Programming 17, 4, 408–461.CrossRefGoogle Scholar
Baral, C. 2003. Knowledge Representation, Reasoning and Declarative Problem Solving. Cambridge University Press.Google Scholar
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, 825–885.Google Scholar
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.Google Scholar
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.Google Scholar
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).Google Scholar
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.Google Scholar
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.Google Scholar
Dantzig, G. 1963. Linear Programming and Extensions. Princeton University Press.Google Scholar
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.Google Scholar
Drescher, C. and Walsh, T. 2010. A translational approach to constraint answer set solving. Theory and Practice of Logic Programming 10, 4–6, 465–480.Google Scholar
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.Google Scholar
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.Google Scholar
Gebser, M., Kaufmann, B. and Schaub, T. 2012. Conflict-driven answer set solving: From theory to practice. Artificial Intelligence 187–188, 52–89.Google Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical negation in logic programs and disjunctive databases. New Generation Computing 9, 365–385.Google Scholar
Goldberg, D. 1991. What every computer scientist should know about floating-point arithmetic. ACM Computing Surveys (CSUR) 23, 1, 5–48.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Simons, P., Niemelä, I. and Soininen, T. 2002. Extending and implementing the stable model semantics. Artificial Intelligence 138, 1–2, 181–234.Google Scholar
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, 467–487.Google Scholar
Taillard, E. 1993. Benchmarks for basic scheduling problems. European Journal of Operational Research 64, 2, 278–285.Google Scholar
van Loon, J. 1981. Irreducibly inconsistent systems of linear inequalities. European Journal of Operational Research 3, 283–288.Google Scholar