{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:01:16Z","timestamp":1747173676019,"version":"3.40.5"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T00:00:00Z","timestamp":1668470400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>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.<\/jats:p>","DOI":"10.1017\/s1471068422000400","type":"journal-article","created":{"date-parts":[[2022,11,15]],"date-time":"2022-11-15T12:39:10Z","timestamp":1668515950000},"page":"1248-1280","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Unifying Framework for Optimizations in Non-Boolean Formalisms"],"prefix":"10.1017","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6146-623X","authenticated-orcid":false,"given":"YULIYA","family":"LIERLER","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,11,15]]},"reference":[{"key":"S1471068422000400_ref9","unstructured":"Brewka, G. and Eiter, T. 2007. Equilibria in heterogeneous nonmonotonic multi-context systems. 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In Proceedings of the 16th International Conference on Principles of Knowledge Representation and Reasoning (KR)."},{"key":"S1471068422000400_ref5","unstructured":"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."},{"key":"S1471068422000400_ref12","unstructured":"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\u2013Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2:1\u20132:15."},{"key":"S1471068422000400_ref17","unstructured":"Lierler, Y. 2022. An abstract view on optimizations in propositional frameworks. Unpublished draft available at https:\/\/arxiv.org\/abs\/2206.06440."},{"volume-title":"Combinatorial Optimization: Algorithms and Complexity","year":"1982","author":"Papadimitriou","key":"S1471068422000400_ref24"},{"key":"S1471068422000400_ref4","unstructured":"Barrett, C. , Fontaine, P. and Tinelli, C. 2016. The Satisfiability Modulo Theories Library (SMT-LIB). www.SMT-LIB.org."},{"key":"S1471068422000400_ref25","unstructured":"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)."},{"first-page":"337","year":"2008","author":"de Moura","key":"S1471068422000400_ref11"},{"first-page":"194","year":"2015","author":"Bj\u00f8rner","key":"S1471068422000400_ref7"},{"key":"S1471068422000400_ref16","doi-asserted-by":"crossref","unstructured":"Lierler, Y. 2021. An abstract view on optimizations in SAT and ASP. 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