{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:55:40Z","timestamp":1760057740512,"version":"build-2065373602"},"reference-count":97,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T00:00:00Z","timestamp":1740009600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Data integrity is crucial for ensuring data correctness and quality and is maintained through integrity constraints that must be continuously checked, especially in data-intensive systems like OLTP. While DBMSs handle very simple cases of constraints (such as primary key and foreign key constraints) well, more complex constraints often require ad hoc solutions. Research since the 1980s has focused on automatic and simplified integrity constraint checking, leveraging the assumption that databases are consistent before updates. This paper presents program transformation operators to generate simplified integrity constraints, focusing on complex constraints expressed in denial form. In particular, we target a class of integrity constraints, called extended denials, which are more general than tuple-generating dependencies and equality-generating dependencies. One of the main contributions of this study consists in the automatic treatment of such a general class of constraints, encompassing the all the most useful and common cases of constraints adopted in practice. Another contribution is the applicability of the proposed technique with a \u201cpreventive\u201d approach; unlike all other methods for integrity maintenance, we check whether an update will violate the constraints before executing it, so we never have to undo any work, with potentially huge savings in terms of execution overhead. These techniques can be readily applied to standard database practices and can be directly translated into SQL.<\/jats:p>","DOI":"10.3390\/a18030123","type":"journal-article","created":{"date-parts":[[2025,2,20]],"date-time":"2025-02-20T11:03:37Z","timestamp":1740049417000},"page":"123","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Simplified Integrity Checking for an Expressive Class of Denial Constraints"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2726-7683","authenticated-orcid":false,"given":"Davide","family":"Martinenghi","sequence":"first","affiliation":[{"name":"Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Piazza Leonardo 32, 20133 Milan, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/BF00263192","article-title":"Logic for Improving Integrity Checking in Relational Data Bases","volume":"18","author":"Nicolas","year":"1982","journal-title":"Acta Inform."},{"key":"ref_2","unstructured":"Schkolnick, M. (1982, January 2\u20134). Fast Methods for Testing Quantified Relational Calculus Assertions. Proceedings of the 1982 ACM SIGMOD International Conference on Management of Data, Orlando, FL, USA."},{"key":"ref_3","first-page":"145","article-title":"Compiling Constraint-Checking Programs from First-Order Formulas","volume":"Volume 2","author":"Gallaire","year":"1984","journal-title":"Proceedings of the Advances in Database Theory"},{"key":"ref_4","unstructured":"Navathe, S.B. (1985, January 28\u201331). Integrity Checking for Multiple Updates. Proceedings of the 1985 ACM SIGMOD International Conference on Management of Data, Austin, TX, USA."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0743-1066(87)90009-4","article-title":"Integrity Constraint Checking in Stratified Databases","volume":"4","author":"Lloyd","year":"1987","journal-title":"J. Log. Program."},{"key":"ref_6","unstructured":"Qian, X. (1988, January 1\u20135). An Effective Method for Integrity Constraint Simplification. Proceedings of the Fourth International Conference on Data Engineering, Los Angeles, CA, USA."},{"key":"ref_7","unstructured":"Minker, J. (1988). A Theorem-Proving Approach to Database Integrity. Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1145\/78922.78924","article-title":"Logic-based approach to semantic query optimization","volume":"15","author":"Chakravarthy","year":"1990","journal-title":"ACM Trans. Database Syst. TODS"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Van Hentenryck, P. (1994). A Slick Procedure for Integrity Checking in Deductive Databases. Logic Programming, Proceedings of the 11th International Conference on Logic Programming, Santa Margherita Ligure, Italy, 13\u201318 June 1994, MIT Press.","DOI":"10.7551\/mitpress\/4316.003.0047"},{"key":"ref_10","unstructured":"Vijayaraman, T.M., Buchmann, A.P., Mohan, C., and Sarda, N.L. (1996, January 3\u20136). Further Improvements on Integrity Constraint Checking for Stratifiable Deductive Databases. Proceedings of the VLDB\u201996, Proceedings of 22th International Conference on Very Large Data Bases, Mumbai, India."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0743-1066(97)10012-7","article-title":"Creating Specialised Integrity Checks Through Partial Evaluation of Meta-Interpreters","volume":"36","author":"Leuschel","year":"1998","journal-title":"J. Log. Program."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0169-023X(99)00007-5","article-title":"Three Types of Redundancy in Integrity Checking: An Optimal Solution","volume":"30","year":"1999","journal-title":"Data Knowl. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Doorn, J.H., and Rivero, L.C. (2002). Translating advanced integrity checking technology to SQL. Database Integrity: Challenges and Solutions, Idea Group Publishing.","DOI":"10.4018\/978-1-93070-838-9"},{"key":"ref_14","unstructured":"Barcel\u00f3, P., S\u00e1nchez-Pi, N., Meliou, A., and Sudarshan, S. (2024, January 9\u201315). PG-Triggers: Triggers for Property Graphs. Proceedings of the Companion of the 2024 International Conference on Management of Data, SIGMOD\/PODS 2024, Santiago, Chile."},{"key":"ref_15","unstructured":"Martinenghi, D. (2005). Advanced Techniques for Efficient Data Integrity Checking. [Ph.D. Thesis, Department of Computer Science, Roskilde University]."},{"key":"ref_16","first-page":"178","article-title":"Simplification of Database Integrity Constraints Revisited: A Transformational Approach","volume":"Volume 3018","author":"Bruynooghe","year":"2003","journal-title":"Logic Based Program Synthesis and Transformation, Proceedings of the 13th International Symposium LOPSTR 2003, Uppsala, Sweden, 25\u201327 August 2003"},{"key":"ref_17","unstructured":"Chandra, A.K., and Merlin, P.M. (1977, January 4\u20136). Optimal implementation of conjunctive queries in relational databases. Proceedings of the 9th Annual ACM Symposium on Theory of Computing, ACM, Boulder, CO, USA."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Shmueli, O. (1987, January 23\u201325). Decidability and expressiveness aspects of logic queries. Proceedings of the Sixth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, San Diego, CA, USA.","DOI":"10.1145\/28659.28685"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1007\/978-3-540-87877-3_24","article-title":"Conjunctive Query Containment under Access Limitations","volume":"Volume 5231","author":"Li","year":"2008","journal-title":"Proceedings of the Conceptual Modeling\u2014ER 2008, 27th International Conference on Conceptual Modeling"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1145\/210197.210200","article-title":"Efficient Checking of Temporal Integrity Constraints Using Bounded History Encoding","volume":"20","author":"Chomicki","year":"1995","journal-title":"ACM Trans. Database Syst. TODS"},{"key":"ref_21","unstructured":"Abbadi, A.E., Brodie, M.L., Chakravarthy, S., Dayal, U., Kamel, N., Schlageter, G., and Whang, K.Y. (2000, January 10\u201314). Temporal Integrity Constraints with Indeterminacy. Proceedings of the VLDB 2000\u201426th International Conference on Very Large Data Bases, Cairo, Egypt."},{"key":"ref_22","first-page":"165","article-title":"An Application of Deontic Logic to Information System Constraints","volume":"48","author":"Carmo","year":"2001","journal-title":"Fundam. Inform."},{"key":"ref_23","unstructured":"Aref, W.G. (2001, January 21\u201324). Exploiting constraint-like data characterizations in query optimization. Proceedings of the SIGMOD \u201901: 2001 ACM SIGMOD International Conference on Management of Data, Santa Barbara, CA, USA."},{"key":"ref_24","unstructured":"Krr, N., and Zilberstein, S. (2006, January 16\u201320). Scoring-based methods for preference representation and reasoning. Proceedings of the 21st National Conference on Artificial Intelligence (AAAI), Boston, MA, USA."},{"key":"ref_25","first-page":"58","article-title":"Preference handling: An AI perspective","volume":"28","author":"Brafman","year":"2006","journal-title":"AI Mag."},{"key":"ref_26","unstructured":"Parsons, S., and Wooldridge, M. (2002, January 13\u201316). Scoring functions for user preference modeling. Proceedings of the ACM International Conference on Intelligent User Interfaces (IUI), San Francisco, CA, USA."},{"key":"ref_27","first-page":"573","article-title":"Preference handling in database systems","volume":"25","author":"Faulkner","year":"2016","journal-title":"VLDB J."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kiessling, W. (2002, January 20\u201323). Foundations of preferences in database systems. Proceedings of the 28th International Conference on Very Large Databases (VLDB), Hong Kong, China.","DOI":"10.1016\/B978-155860869-6\/50035-4"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1145\/958942.958946","article-title":"Preference formulas in relational queries","volume":"28","author":"Chomicki","year":"2003","journal-title":"ACM Trans. Database Syst. TODS"},{"key":"ref_30","unstructured":"Agrawal, R., and Wimmers, E.L. (2005, January 14\u201316). Preference SQL: Flexible preference queries in databases. Proceedings of the 2005 ACM SIGMOD International Conference on Management of Data, Baltimore, MD, USA."},{"key":"ref_31","unstructured":"Tan, W., Guerrini, G., Catania, B., and Gounaris, A. (2013, January 18\u201322). Access patterns and integrity constraints revisited. Proceedings of the Joint 2013 EDBT\/ICDT Conferences, ICDT \u201913 Proceedings, Genoa, Italy."},{"key":"ref_32","unstructured":"Rustin, R. (1971, January 24\u201325). Further normalization of the database relational model. Proceedings of the Courant Computer Science Symposium 6: Data Base Systems, New York, NY, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1145\/320557.320571","article-title":"Multivalued Dependencies and a New Normal Form for Relational Databases","volume":"2","author":"Fagin","year":"1977","journal-title":"ACM Trans. Database Syst. TODS"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"952","DOI":"10.1145\/322344.322347","article-title":"Horn clauses and database dependencies","volume":"29","author":"Fagin","year":"1982","journal-title":"J. ACM"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"718","DOI":"10.1145\/1634.1636","article-title":"A Proof Procedure for Data Dependencies","volume":"31","author":"Beeri","year":"1984","journal-title":"J. ACM"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1016\/j.tcs.2004.10.033","article-title":"Data exchange: Semantics and query answering","volume":"336","author":"Fagin","year":"2005","journal-title":"Theor. Comput. Sci."},{"key":"ref_37","unstructured":"Ullman, J.D. (1988). Principles of Database and Knowledge-Base Systems, Volume I, Computer Science Press."},{"key":"ref_38","unstructured":"Ullman, J.D. (1989). Principles of Database and Knowledge-Base Systems, Volume II, Computer Science Press."},{"key":"ref_39","unstructured":"Agrawal, R., Baker, S., and Bell, D.A. (1993, January 24\u201327). Combining Theory and Practice in Integrity Control: A Declarative Approach to the Specification of a Transaction Modification Subsystem. Proceedings of the 19th International Conference on Very Large Data Bases, Dublin, Ireland."},{"key":"ref_40","unstructured":"Arenas, M., Bertossi, L.E., and Chomicki, J. (June, January 31). Consistent Query Answers in Inconsistent Databases. Proceedings of the Eighteenth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Philadelphia, PA, USA."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Cal\u00ec, A., Lembo, D., and Rosati, R. (2003, January 9\u201312). On the decidability and complexity of query answering over inconsistent and incomplete databases. Proceedings of the PODS \u201903: Twenty-Second ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, New York, NY, USA.","DOI":"10.1145\/773153.773179"},{"key":"ref_42","first-page":"14","article-title":"Database Repair by Signed Formulae","volume":"Volume 2942","author":"Seipel","year":"2004","journal-title":"Proceedings of the Foundations of Information and Knowledge Systems, Third International Symposium (FoIKS 2004)"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Bertossi, L.E. (2011). Database Repairing and Consistent Query Answering, Morgan & Claypool Publishers. Synthesis Lectures on Data Management.","DOI":"10.1007\/978-3-031-01883-1"},{"key":"ref_44","unstructured":"Suciu, D., Skritek, S., and Koch, C. (July, January 30). Database Repairs and Consistent Query Answering: Origins and Further Developments. Proceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS, Amsterdam, The Netherlands."},{"key":"ref_45","first-page":"287","article-title":"A Relaxed Approach to Integrity and Inconsistency in Databases","volume":"Volume 4246","author":"Hermann","year":"2006","journal-title":"Proceedings of the Logic for Programming, Artificial Intelligence, and Reasoning, 13th International Conference, LPAR 2006"},{"key":"ref_46","unstructured":"Decker, H., and Martinenghi, D. (2006, January 4\u20138). Avenues to Flexible Data Integrity Checking. Proceedings of the 17th International Workshop on Database and Expert Systems Applications (DEXA 2006), Krakow, Poland."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Decker, H., and Martinenghi, D. (2007, January 3\u20137). Getting Rid of Straitjackets for Flexible Integrity Checking. Proceedings of the 18th International Workshop on Database and Expert Systems Applications (DEXA 2007), Regensburg, Germany.","DOI":"10.1109\/DEXA.2007.4312917"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/s10844-006-2974-4","article-title":"Measuring inconsistency in knowledgebases","volume":"27","author":"Grant","year":"2006","journal-title":"J. Intell. Inf. Syst."},{"key":"ref_49","unstructured":"Walsh, T. (2011, January 16\u201322). Measuring the Good and the Bad in Inconsistent Information. Proceedings of the IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain."},{"key":"ref_50","first-page":"230","article-title":"Distance-Based Measures of Inconsistency","volume":"Volume 7958","year":"2013","journal-title":"Proceedings of the Symbolic and Quantitative Approaches to Reasoning with Uncertainty\u201412th European Conference, ECSQARU 2013"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.ijar.2016.04.004","article-title":"Analysing inconsistent information using distance-based measures","volume":"89","author":"Grant","year":"2017","journal-title":"Int. J. Approx. Reason."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.ijar.2023.02.008","article-title":"Semantic inconsistency measures using 3-valued logics","volume":"156","author":"Grant","year":"2023","journal-title":"Int. J. Approx. Reason."},{"key":"ref_53","first-page":"31","article-title":"Simplification of Integrity Constraints for Data Integration","volume":"Volume 2942","author":"Seipel","year":"2004","journal-title":"Proceedings of the Foundations of Information and Knowledge Systems, Third International Symposium, FoIKS 2004"},{"key":"ref_54","first-page":"348","article-title":"Simplification of Integrity Constraints with Aggregates and Arithmetic Built-Ins","volume":"Volume 3055","author":"Christiansen","year":"2004","journal-title":"Proceedings of the Flexible Query Answering Systems, 6th International Conference, FQAS 2004"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"74068","DOI":"10.1109\/ACCESS.2021.3079799","article-title":"Integrity Checking for Aggregate Queries","volume":"9","author":"Samarin","year":"2021","journal-title":"IEEE Access"},{"key":"ref_56","first-page":"606","article-title":"Transaction Management with Integrity Checking","volume":"Volume 3588","author":"Andersen","year":"2005","journal-title":"Proceedings of the Database and Expert Systems Applications, 16th International Conference, DEXA 2005"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1080\/088395100117034","article-title":"Symbolic Constraints for Meta-Logic Programming","volume":"14","author":"Christiansen","year":"2000","journal-title":"Appl. Artif. Intell."},{"key":"ref_58","first-page":"18:1","article-title":"Integrity Constraints Revisited: From Exact to Approximate Implication","volume":"Volume 155","author":"Lutz","year":"2020","journal-title":"Proceedings of the 23rd International Conference on Database Theory, ICDT 2020"},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1658","DOI":"10.1109\/TNSE.2021.3068261","article-title":"Efficient Continuous Big Data Integrity Checking for Decentralized Storage","volume":"8","author":"Yu","year":"2021","journal-title":"IEEE Trans. Netw. Sci. Eng."},{"key":"ref_60","first-page":"615","article-title":"Data Integrity Checking Supporting Reliable Data Migration in Cloud Storage","volume":"Volume 12384","author":"Yu","year":"2020","journal-title":"Proceedings of the Wireless Algorithms, Systems, and Applications\u201415th International Conference, WASA 2020"},{"key":"ref_61","first-page":"358","article-title":"Trajectory Clustering via Effective Partitioning","volume":"Volume 5822","author":"Andreasen","year":"2009","journal-title":"Proceedings of the Flexible Query Answering Systems, 8th International Conference, FQAS 2009"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1016\/j.ins.2013.12.003","article-title":"Analysing microarray expression data through effective clustering","volume":"262","author":"Masciari","year":"2014","journal-title":"Inf. Sci."},{"key":"ref_63","first-page":"113","article-title":"A Deep Learning Approach to Fake News Detection","volume":"Volume 12117","author":"Helic","year":"2020","journal-title":"Proceedings of the Foundations of Intelligent Systems\u201425th International Symposium, ISMIS 2020"},{"key":"ref_64","unstructured":"Desai, B.C., and Cho, W. (2020, January 12\u201314). Detecting fake news by image analysis. Proceedings of the IDEAS 2020: 24th International Database Engineering & Applications Symposium, Seoul, Republic of Korea."},{"key":"ref_65","unstructured":"Desai, B.C., Sacc\u00e0, D., and Greco, S. (2009, January 16\u201318). Efficient and effective RFID data warehousing. Proceedings of the International Database Engineering and Applications Symposium (IDEAS 2009), Cetraro, Italy. International Conference Proceeding Series."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1145\/2487259.2487263","article-title":"RFID-data compression for supporting aggregate queries","volume":"38","author":"Fazzinga","year":"2013","journal-title":"ACM Trans. Database Syst."},{"key":"ref_67","unstructured":"Desai, B.C., Larriba-Pey, J.L., and Bernardino, J. (2013, January 9\u201311). Sequential pattern mining from trajectory data. Proceedings of the 17th International Database Engineering & Applications Symposium, IDEAS \u201913, Barcelona, Spain."},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Galli, L., Fraternali, P., Martinenghi, D., Tagliasacchi, M., and Novak, J. (2012, January 3\u20135). A Draw-and-Guess Game to Segment Images. Proceedings of the 2012 International Conference on Privacy, Security, Risk and Trust, PASSAT 2012, and 2012 International Confernece on Social Computing, SocialCom 2012, Amsterdam, The Netherlands.","DOI":"10.1109\/SocialCom-PASSAT.2012.139"},{"key":"ref_69","unstructured":"Bozzon, A., Catallo, I., Ciceri, E., Fraternali, P., Martinenghi, D., and Tagliasacchi, M. (2012, January 17). A Framework for Crowdsourced Multimedia Processing and Querying. Proceedings of the First International Workshop on Crowdsourcing Web Search, Lyon, France. CEUR Workshop Proceedings."},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Loni, B., Menendez, M., Georgescu, M., Galli, L., Massari, C., Alting\u00f6vde, I.S., Martinenghi, D., Melenhorst, M., Vliegendhart, R., and Larson, M. (March, January 27). Fashion-focused creative commons social dataset. Proceedings of the Multimedia Systems Conference 2013, MMSys \u201913, Oslo, Norway.","DOI":"10.1145\/2483977.2483984"},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10844-013-0267-2","article-title":"Dealing with trajectory streams by clustering and mathematical transforms","volume":"42","author":"Costa","year":"2014","journal-title":"J. Intell. Inf. Syst."},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jpdc.2021.02.012","article-title":"RDIC: A blockchain-based remote data integrity checking scheme for IoT in 5G networks","volume":"152","author":"Wang","year":"2021","journal-title":"J. Parallel Distrib. Comput."},{"key":"ref_73","unstructured":"Srivastava, S.S., Atre, M., Sharma, S., Gupta, R., and Shukla, S.K. (2019). Verity: Blockchains to Detect Insider Attacks in DBMS. arXiv."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1007\/s10586-021-03408-y","article-title":"Flexible identity-based remote data integrity checking for cloud storage with privacy preserving property","volume":"25","author":"Ji","year":"2022","journal-title":"Clust. Comput."},{"key":"ref_75","doi-asserted-by":"crossref","unstructured":"Bienvenu, M., and Bourgaux, C. (2023). Inconsistency Handling in Prioritized Databases with Universal Constraints: Complexity Analysis and Links with Active Integrity Constraints. arXiv.","DOI":"10.24963\/kr.2023\/10"},{"key":"ref_76","unstructured":"Nilsson, U., and Ma\u0142uzy\u0144ski, J. (1995). Logic, Programming and Prolog, John Wiley & Sons Ltd.. [2nd ed.]."},{"key":"ref_77","doi-asserted-by":"crossref","unstructured":"Lloyd, J. (1987). Foundations of Logic Programming, Springer. [2nd ed.].","DOI":"10.1007\/978-3-642-83189-8"},{"key":"ref_78","unstructured":"Minker, J. (1988). Towards a Theory of Declarative Knowledge. Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0743-1066(94)90024-8","article-title":"Logic Programming and Negation: A Survey","volume":"19\/20","author":"Apt","year":"1994","journal-title":"J. Log. Program."},{"key":"ref_80","doi-asserted-by":"crossref","unstructured":"Minker, J. (1988). On the declarative semantics of deductive databases and logic programming. Foundations of Deductive Databases and Logic Programming, Morgan Kaufmann.","DOI":"10.1016\/0743-1066(88)90006-4"},{"key":"ref_81","unstructured":"Kowalski, R., and Bowen, K. (1988). Minimal Model Semantics for Logic Programming. Logic Programming: Proceedings of the Fifth Logic Programming Symposium, MIT Press."},{"key":"ref_82","doi-asserted-by":"crossref","unstructured":"van Gelder, A., Ross, K., and Schlipf, J.S. (1988, January 21\u201323). Unfounded sets and well-founded semantics for general logic programs. Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems (PODS 88), Austin, TX, USA.","DOI":"10.1145\/308386.308444"},{"key":"ref_83","unstructured":"Dijkstra, E.W. (1976). A Discipline of Programming, Prentice-Hall."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1145\/363235.363259","article-title":"An axiomatic basis for computer programming","volume":"12","author":"Hoare","year":"1969","journal-title":"Commun. ACM"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/0743-1066(93)90022-9","article-title":"Loop checking in partial deduction","volume":"16","author":"Bol","year":"1993","journal-title":"J. Log. Program."},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1145\/131295.131297","article-title":"The impact of logic programming on databases","volume":"35","author":"Grant","year":"1992","journal-title":"Commun. ACM CACM"},{"key":"ref_87","unstructured":"Adeli, H. (1990). Integrity Constraints in Knowledge Based Systems. Knowledge Engineering Vol II, Applications, McGraw-Hill."},{"key":"ref_88","doi-asserted-by":"crossref","unstructured":"Gabbay, D.M., Hogger, C.J., and Robinson, J.A. (1993). Deduction Systems Based on Resolution. Handbook of Logic in Artificial Intelligence and Logic Programming\u2014Vol 1: Logical Foundations, Clarendon Press.","DOI":"10.1093\/oso\/9780198537458.001.0001"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1145\/321250.321253","article-title":"A Machine-Oriented Logic Based on the Resolution Principle","volume":"12","author":"Robinson","year":"1965","journal-title":"J. ACM"},{"key":"ref_90","unstructured":"Chang, C.L., and Lee, R.C. (1973). Symbolic Logic and Mechanical Theorem Proving, Academic Press."},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/0304-3975(87)90113-7","article-title":"Domain-Independent Formulas and Databases","volume":"52","author":"Topor","year":"1987","journal-title":"Theor. Comput. Sci."},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/0743-1066(84)90011-6","article-title":"Making Prolog more Expressive","volume":"3","author":"Lloyd","year":"1984","journal-title":"J. Log. Program."},{"key":"ref_93","unstructured":"(2025, February 17). Information Technology\u2014Database Languages\u2014GQL. Available online: https:\/\/www.iso.org\/standard\/76120.html."},{"key":"ref_94","doi-asserted-by":"crossref","unstructured":"Magnanimi, D., Bellomarini, L., Ceri, S., and Martinenghi, D. (2023, January 3\u20137). Reactive Company Control in Company Knowledge Graphs. Proceedings of the 39th IEEE International Conference on Data Engineering, ICDE 2023, Anaheim, CA, USA.","DOI":"10.1109\/ICDE55515.2023.00256"},{"key":"ref_95","unstructured":"Baldazzi, T., and Sallinger, E. (2025, February 17). iWarded. Available online: https:\/\/github.com\/joint-kg-labs\/iWarded."},{"key":"ref_96","unstructured":"Snodgrass, R.T., and Winslett, M. (1994, January 24\u201327). Optimization of Dynamic Query Evaluation Plans. Proceedings of the 1994 ACM SIGMOD International Conference on Management of Data, Minneapolis, MN, USA."},{"key":"ref_97","unstructured":"Jagadish, H.V., and Mumick, I.S. (1996, January 4\u20136). Cost-Based Optimization for Magic: Algebra and Implementation. Proceedings of the 1996 ACM SIGMOD International Conference on Management of Data, Montreal, QC, Canada."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/3\/123\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:39:02Z","timestamp":1760027942000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/3\/123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,20]]},"references-count":97,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["a18030123"],"URL":"https:\/\/doi.org\/10.3390\/a18030123","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2025,2,20]]}}}