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At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make the semantic characterization of clingo\u2019s theory-reasoning framework precise. This provides us with a formal framework in which we can elaborate upon the formal properties of existing hybridizations of clingo, such as clingcon, clingo[dl], and clingo[lp].<\/jats:p>","DOI":"10.3390\/a16040185","type":"journal-article","created":{"date-parts":[[2023,3,29]],"date-time":"2023-03-29T01:33:00Z","timestamp":1680053580000},"page":"185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["On the Semantics of Hybrid ASP Systems Based on Clingo"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7440-0953","authenticated-orcid":false,"given":"Pedro","family":"Cabalar","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Corunna, 15008 A Corunna, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3917-8717","authenticated-orcid":false,"given":"Jorge","family":"Fandinno","sequence":"additional","affiliation":[{"name":"College of Information Science & Technology, University of Nebraska at Omaha, Omaha, NE 68182, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7456-041X","authenticated-orcid":false,"given":"Torsten","family":"Schaub","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Potsdam, 14469 Potsdam, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4986-4881","authenticated-orcid":false,"given":"Philipp","family":"Wanko","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Potsdam, 14469 Potsdam, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,3,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1007\/978-3-642-15025-8_24","article-title":"Thirteen Definitions of a Stable Model","volume":"Volume 6300","author":"Blass","year":"2010","journal-title":"Fields of Logic and Computation, Essays Dedicated to Yuri Gurevich on the Occasion of His 70th Birthday"},{"key":"ref_2","unstructured":"Kowalski, R., and Bowen, K. (1988, January 15\u201319). The Stable Model Semantics for Logic Programming. Proceedings of the Fifth International Conference and Symposium of Logic Programming (ICLP\u201988), Seattle, WA, USA."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1017\/S1471068415000150","article-title":"Abstract Gringo","volume":"15","author":"Gebser","year":"2015","journal-title":"Theory Pract. Log. Program."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/s13218-018-0548-6","article-title":"Industrial Applications of Answer Set Programming","volume":"32","author":"Falkner","year":"2018","journal-title":"K\u00fcnstliche Intell."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.artint.2013.10.004","article-title":"Relating constraint answer set programming languages and algorithms","volume":"207","author":"Lierler","year":"2014","journal-title":"Artif. Intell."},{"key":"ref_6","first-page":"167","article-title":"A Tutorial on Hybrid Answer Set Solving with clingo","volume":"Volume 10370","author":"Ianni","year":"2017","journal-title":"Proceedings of the Thirteenth International Summer School of the Reasoning Web"},{"key":"ref_7","first-page":"825","article-title":"Satisfiability Modulo Theories","volume":"Volume 185","author":"Biere","year":"2009","journal-title":"Handbook of Satisfiability"},{"key":"ref_8","first-page":"73","article-title":"Smodels with CLP and Its Applications: A Simple and Effective Approach to Aggregates in ASP","volume":"Volume 3132","author":"Demoen","year":"2004","journal-title":"Proceedings of the Twentieth International Conference on Logic Programming (ICLP\u201904)"},{"key":"ref_9","first-page":"235","article-title":"Constraint Answer Set Solving","volume":"Volume 5649","author":"Hill","year":"2009","journal-title":"Proceedings of the Twenty-Fifth International Conference on Logic Programming (ICLP\u201909)"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1017\/S1471068410000220","article-title":"A Translational Approach to Constraint Answer Set Solving","volume":"10","author":"Drescher","year":"2010","journal-title":"Theory Pract. Log. Program."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1017\/S1471068412000142","article-title":"ASP modulo CSP: The clingcon system","volume":"12","author":"Ostrowski","year":"2012","journal-title":"Theory Pract. Log. Program."},{"key":"ref_12","unstructured":"Inclezan, D., and Maratea, M. (2015). Proceedings of the Eighth Workshop on Answer Set Programming and Other Computing Paradigms (ASPOCP\u201915), Cork, Ireland, 13 August 2015."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1017\/S1471068417000138","article-title":"Clingcon: The Next Generation","volume":"17","author":"Banbara","year":"2017","journal-title":"Theory Pract. Log. Program."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"872","DOI":"10.1017\/S1471068417000242","article-title":"Clingo goes Linear Constraints over Reals and Integers","volume":"17","author":"Janhunen","year":"2017","journal-title":"Theory Pract. Log. Program."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1007\/s13218-018-0535-y","article-title":"The DLVHEX System","volume":"32","author":"Eiter","year":"2018","journal-title":"K\u00fcnstliche Intell."},{"key":"ref_16","unstructured":"Gebser, M., Kaminski, R., Kaufmann, B., Ostrowski, M., Schaub, T., and Wanko, P. (2016, January 16\u201321). Theory Solving Made Easy with Clingo 5. Proceedings of the Technical Communications of the Thirty-Second International Conference on Logic Programming (ICLP\u201916), New York, NY, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10472-006-9028-z","article-title":"Equilibrium logic","volume":"47","author":"Pearce","year":"2006","journal-title":"Ann. Math. Artif. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1017\/S1471068421000478","article-title":"Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches","volume":"23","author":"Lierler","year":"2023","journal-title":"Theory Pract. Log. Program."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"462","DOI":"10.1017\/S1471068417000102","article-title":"Constraint answer set solver EZCSP and why integration schemas matter","volume":"17","author":"Balduccini","year":"2017","journal-title":"Theory Pract. Log. Program."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1007\/978-3-642-04238-6_14","article-title":"Computing Stable Models via Reductions to Difference Logic","volume":"Volume 5753","author":"Erdem","year":"2009","journal-title":"Proceedings of the Tenth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR\u201909)"},{"key":"ref_21","unstructured":"Brewka, G., Eiter, T., and McIlraith, S. (2012, January 10\u201314). Answer Set Programming via Mixed Integer Programming. Proceedings of the Thirteenth International Conference on Principles of Knowledge Representation and Reasoning (KR\u201912), Rome, Italy."},{"key":"ref_22","first-page":"1:1","article-title":"SMT-Based Constraint Answer Set Solver EZSMT (System Description)","volume":"46","author":"Lierler","year":"2016","journal-title":"Comput. Sci. Fac. Proc. Present."},{"key":"ref_23","unstructured":"Kaelbling, L., and Saffiotti, A. (August, January 30). A Uniform Integration of Higher-Order Reasoning and External Evaluations in Answer-Set Programming. Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence (IJCAI\u201905), Scotland, UK."},{"key":"ref_24","unstructured":"Brewka, G., and Eiter, T. (2007, January 22\u201326). Equilibria in Heterogeneous Nonmonotonic Multi-Context Systems. Proceedings of the Twenty-Second National Conference on Artificial Intelligence (AAAI\u201907), Vancouver, BC, Canada."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1017\/S1471068410000517","article-title":"Functional answer set programming","volume":"11","author":"Cabalar","year":"2011","journal-title":"Theory Pract. Log. Program."},{"key":"ref_26","unstructured":"Balduccini, M., and Gelfond, M. (2013). Language ASP{f} with Arithmetic Expressions and Consistency-Restoring Rules. arXiv."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.artint.2019.01.001","article-title":"First-order stable model semantics with intensional functions","volume":"273","author":"Bartholomew","year":"2019","journal-title":"Artif. Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1017\/S1471068418000169","article-title":"Functional ASP with Intensional Sets: Application to Gelfond-Zhang Aggregates","volume":"18","author":"Cabalar","year":"2018","journal-title":"Theory Pract. Log. Program."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1007\/978-3-642-30743-0_3","article-title":"A \u201cconservative\u201d approach to extending answer set programming with nonherbrand functions","volume":"Volume 7265","author":"Erdem","year":"2012","journal-title":"Correct Reasoning: Essays on Logic-Based AI in Honour of Vladimir Lifschitz"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1017\/S1471068413000549","article-title":"On the stable model semantics for intensional functions","volume":"13","author":"Bartholomew","year":"2013","journal-title":"Theory Pract. Log. Program."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1017\/S1471068413000343","article-title":"ASP with non-herbrand partial functions: A language and system for practical use","volume":"13","author":"Balduccini","year":"2013","journal-title":"Theory Pract. Log. Program."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1017\/S1471068418000285","article-title":"Constraint Answer Set Programming without Grounding","volume":"18","author":"Arias","year":"2018","journal-title":"Theory Pract. Log. Program."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1017\/S1471068420000393","article-title":"ASP(AC): Answer Set Programming with Algebraic Constraints","volume":"20","author":"Eiter","year":"2020","journal-title":"Theory Pract. Log. Program."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"526","DOI":"10.1145\/383779.383783","article-title":"Strongly equivalent logic programs","volume":"2","author":"Lifschitz","year":"2001","journal-title":"ACM Trans. Comput. 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