Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-19T15:24:59.941Z Has data issue: false hasContentIssue false
  • English
  • Français

Unifying Framework for Optimizations in Non-Boolean Formalisms

Published online by Cambridge University Press:  15 November 2022

YULIYA LIERLER Open the ORCID record for YULIYA LIERLER [Opens in a new window]
YULIYA LIERLER*
Affiliation:
University of Nebraska Omaha, Omaha, NE 68182, USA (e-mail: ylierler@unomaha.edu)
Get access Rights & Permissions [Opens in a new window]

Abstract

Search-optimization problems are plentiful in scientific and engineering domains. Artificial intelligence (AI) has long contributed to the development of search algorithms and declarative programming languages geared toward solving and modeling search-optimization problems. Automated reasoning and knowledge representation are the subfields of AI that are particularly vested in these developments. Many popular automated reasoning paradigms provide users with languages supporting optimization statements. Recall integer linear programming, MaxSAT, optimization satisfiability modulo theory, (constraint) answer set programming. These paradigms vary significantly in their languages in ways they express quality conditions on computed solutions. Here we propose a unifying framework of so-called extended weight systems that eliminates syntactic distinctions between paradigms. They allow us to see essential similarities and differences between optimization statements provided by distinct automated reasoning languages. We also study formal properties of the proposed systems that immediately translate into formal properties of paradigms that can be captured within our framework.

Keywords

designanalysis and implementation of languagesknowledge representation and nonmonotonic reasoningtheory
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 23 , Issue 6 , November 2023 , pp. 1248 - 1280
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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.)

Footnotes

*

The work was partially supported by NSF grant 1707371. We are grateful to anonymous reviewers for valuable comments on this paper.

References

Alviano, M. 2018. Algorithms for solving optimization problems in answer set programming. Intelligenza Artificiale, 12, 1–14.Google Scholar
Alviano, M., Romero, J. and Schaub, T. Preference relations by approximation. In KR 2018. AAAI Press, 2–11.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
Barrett, C., Fontaine, P. and Tinelli, C. 2016. The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org.Google Scholar
Barrett, C., Stump, A. and Tinelli, C. 2010. The SMT-LIB Standard: Version 2.0. In Proceedings of the 8th International Workshop on Satisfiability Modulo Theories (Edinburgh, UK), A. Gupta and D. Kroening, Eds.Google Scholar
Barrett, C. and Tinelli, C. 2014. Satisfiability modulo theories. In Handbook of Model Checking, E. Clarke, T. Henzinger and H. Veith, Eds. Springer.Google Scholar
Bjørner, N., Phan, A.-D. and Fleckenstein, L. 2015. $\nu$ z - an optimizing smt solver. In Tools and Algorithms for the Construction and Analysis of Systems, C. Baier and C. Tinelli, Eds. Springer Berlin Heidelberg, Berlin, Heidelberg, 194–199.Google Scholar
Brewka, G., Delgrande, J. P., Romero, J. and Schaub, T. 2015. asprin: Customizing answer set preferences without a headache. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25–30, 2015, Austin, Texas, USA, 1467–1474.Google Scholar
Brewka, G. and Eiter, T. 2007. Equilibria in heterogeneous nonmonotonic multi-context systems. In Proceedings of National Conference on Artificial Intelligence, AAAI 2007, 385–390.Google Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F. and Schaub, T. 2013. Asp-core-2 input language format. URL: https://www.mat.unical.it/aspcomp2013/files/ASP-CORE-2.03c.pdf.Google Scholar
de Moura, L. and Bjørner, N. 2008. Z3: An efficient smt solver. In Tools and Algorithms for the Construction and Analysis of Systems, C. R. Ramakrishnan and J. Rehof, Eds. Springer Berlin Heidelberg, Berlin, Heidelberg, 337–340.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T. and Wanko, P. 2016. Theory solving made easy with Clingo 5. In Technical Communications of the 32nd International Conference on Logic Programming (ICLP 2016), OpenAccess Series in Informatics (OASIcs), M. Carro, A. King, N. Saeedloei and M. D. Vos, Eds., vol. 52. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2:1–2:15.Google Scholar
Gebser, M., Kaufmann, B., Neumann, A. and Schaub, T. 2007a. Conflict-driven answer set solving. In Proceedings of 20th International Joint Conference on Artificial Intelligence (IJCAI’07). MIT Press, 386–392.Google Scholar
Gebser, M., Schaub, T. and Thiele, S. 2007b. Gringo: A new grounder for answer set programming. In Proceedings of the Ninth International Conference on Logic Programming and Nonmonotonic Reasoning, 266–271.Google Scholar
Lierler, Y. 2014. Relating constraint answer set programming languages and algorithms. Artificial Intelligence, 207C, 1–22.10.1016/j.artint.2013.10.004CrossRefGoogle Scholar
Lierler, Y. 2021. An abstract view on optimizations in SAT and ASP. In Proceedings of the 17th European Conference on Logics in Artificial Intelligence (JELIA).10.1007/978-3-030-75775-5_25CrossRefGoogle Scholar
Lierler, Y. 2022. An abstract view on optimizations in propositional frameworks. Unpublished draft available at https://arxiv.org/abs/2206.06440.Google Scholar
Lierler, Y. and Susman, B. 2017. On relation between constraint answer set programming and satisfiability modulo theories. Theory and Practice of Logic Programming, 17, 4, 559–590.10.1017/S1471068417000114CrossRefGoogle Scholar
Lierler, Y. and Truszczynski, M. 2011. Transition systems for model generators — a unifying approach. Theory and Practice of Logic Programming, 11(4-5), 629–646. (Special Issue, Proceedings of the 27th International Conference on Logic Programming, ICLP 2011).10.1017/S1471068411000214CrossRefGoogle Scholar
Lierler, Y. and Truszczynski, M. 2015. An abstract view on modularity in knowledge representation. In Proceedings of the AAAI Conference on Artificial Intelligence.10.1609/aaai.v29i1.9390CrossRefGoogle Scholar
Lifschitz, V., Tang, L. R. and Turner, H. 1999. Nested expressions in logic programs. Annals of Mathematics and Artificial Intelligence, 25, 369–389.10.1023/A:1018978005636CrossRefGoogle Scholar
Nieuwenhuis, R. and Oliveras, A. 2006. On sat modulo theories and optimization problems. In Theory and Applications of Satisfiability Testing - SAT 2006, A. Biere and C. P. Gomes, Eds. Springer Berlin Heidelberg, Berlin, Heidelberg, 156–169.Google Scholar
Ostrowski, M. and Schaub, T. 2012. Asp modulo csp: The clingcon system. Theory and Practice of Logic Programming, 12, 4–5, 485–503.10.1017/S1471068412000142CrossRefGoogle Scholar
Papadimitriou, C. and Steiglitz, K. 1982. Combinatorial Optimization: Algorithms and Complexity, Prentice-Hall, Inc., USA.Google Scholar
Robinson, N., Gretton, C., Pham, D.-N. and Sattar, A. 2010. Cost-optimal planning using weighted maxsat. In ICAPS 2010 Workshop on Constraint Satisfaction Techniques for Planning and Scheduling (COPLAS10).Google Scholar
Sebastiani, R. and Tomasi, S. 2012. Optimization in smt with la(q) cost functions. In Automated Reasoning, B. Gramlich, D. Miller and U. Sattler, Eds. Springer Berlin Heidelberg, Berlin, Heidelberg, 484–498.Google Scholar
Shen, D. and Lierler, Y. 2018. Smt-based constraint answer set solver ezsmt+ for non-tight programs. In Proceedings of the 16th International Conference on Principles of Knowledge Representation and Reasoning (KR).Google Scholar