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Defeasible Reasoning via Datalog¬

Published online by Cambridge University Press:  02 November 2021

MICHAEL J. MAHER Open the ORCID record for MICHAEL J. MAHER [Opens in a new window]
MICHAEL J. MAHER*
Affiliation:
Reasoning Research Institute Canberra, Australia (e-mail: [email protected])
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Abstract

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We address the problem of compiling defeasible theories to Datalog¬ programs. We prove the correctness of this compilation, for the defeasible logic DL(∂||), but the techniques we use apply to many other defeasible logics. Structural properties of DL(∂||) are identified that support efficient implementation and/or approximation of the conclusions of defeasible theories in the logic, compared with other defeasible logics. We also use previously well-studied structural properties of logic programs to adapt to incomplete Datalog¬ implementations.

Keywords

defeasible logicprogram transformationwell-founded semanticsmeta-programming
Type
Original Article
Information
Theory and Practice of Logic Programming , Volume 23 , Issue 5 , September 2023 , pp. 986 - 1028
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

References

Aberger, C. R., Lamb, A., Tu, S., Nötzli, A., Olukotun, K. and Ré, C. 2017. Emptyheaded: A relational engine for graph processing. ACM Transactions on Database Systems 42, 4, 20:1–20:44.10.1145/3129246CrossRefGoogle Scholar
Abiteboul, S., Hull, R. and Vianu, V. 1995. Foundations of Databases. Addison-Wesley.Google Scholar
Adrian, W. T., Alviano, M., Calimeri, F., Cuteri, B., Dodaro, C., Faber, W., Fuscà, D., Leone, N., Manna, M., Perri, S., Ricca, F., Veltri, P. and Zangari, J. 2018. The ASP system DLV: Advancements and applications. KI 32, 2-3, 177–179.Google Scholar
Alvaro, P., Marczak, W. R., Conway, N., Hellerstein, J. M., Maier, D. and Sears, R. 2010. Dedalus: Datalog in time and space. In Datalog Reloaded - First International Workshop, Datalog 2010, de Moor, O., Gottlob, G., Furche, T., and Sellers, A. J., Eds. Lecture Notes in Computer Science, vol. 6702. Springer, 262–281.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2000. A flexible framework for defeasible logics. In AAAI/IAAI. AAAI Press/The MIT Press, 405–410.Google Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2001. Representation results for defeasible logic. ACM Transactions on Computational Logic 2, 2, 255–287.10.1145/371316.371517CrossRefGoogle Scholar
Antoniou, G., Billington, D., Governatori, G. and Maher, M. J. 2006. Embedding defeasible logic into logic programming. Theory and Practice of Logic Programming 6, 6, 703–735. Antoniou, G., Billington, D., Governatori, G., Maher, M. J. and Rock, A. 2000. A family of defeasible reasoning logics and its implementation. In ECAI, W. Horn, Ed. IOS Press, 459–463.Google Scholar
Antoniou, G. and Maher, M. J. 2002. Embedding defeasible logic into logic programs. In Logic Programming, 18th International Conference. 393–404.Google Scholar
Apt, K. R., Blair, H. A. and Walker, A. 1988. Towards a theory of declarative knowledge. In Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, 89–148.Google Scholar
Apt, K. R. and Bol, R. N. 1994. Logic programming and negation: A survey. Journal of Logical Programming 19/20, 9–71.Google Scholar
Aravindan, C. and Dung, P. M. 1995. On the correctness of unfold/fold transformation of normal and extended logic programs. Journal of Logical Programming 24, 3, 201–217.10.1016/0743-1066(94)00104-ECrossRefGoogle Scholar
Aref, M., ten Cate, B., Green, T. J., Kimelfeld, B., Olteanu, D., Pasalic, E., Veldhuizen, T. L. and Washburn, G. 2015. Design and implementation of the LogicBlox system. In Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data, Sellis, T. K., Davidson, S. B., and Ives, Z. G., Eds. ACM, 1371–1382.Google Scholar
Avgustinov, P., de Moor, O., Jones, M. P. and Schäfer, M. 2016. QL: object-oriented queries on relational data. In 30th European Conference on Object-Oriented Programming, ECOOP 2016, Krishnamurthi, S. and Lerner, B. S., Eds. LIPIcs, vol. 56. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2:1–2:25.Google Scholar
Bassiliades, N., Antoniou, G. and Vlahavas, I. P. 2006. A defeasible logic reasoner for the semantic web. Journal on Semantic Web and Information Systems 2, 1, 1–41.10.4018/jswis.2006010101CrossRefGoogle Scholar
Bellomarini, L., Sallinger, E. and Gottlob, G. 2018. The Vadalog system: Datalog-based reasoning for knowledge graphs. Proceedings of the VLDB Endowment 11, 9, 975–987.Google Scholar
Bembenek, A., Greenberg, M. and Chong, S. 2020. Formulog: Datalog for smt-based static analysis. Proceedings of the ACM on Programming Languages 4, OOPSLA, 141:1–141:31.Google Scholar
Billington, D., Antoniou, G., Governatori, G. and Maher, M. J. 2010. An inclusion theorem for defeasible logics. ACM Transactions on Computational Logic 12, 1, 6.10.1145/1838552.1838558CrossRefGoogle Scholar
Billington, D. and Rock, A. 2001. Propositional plausible logic: Introduction and implementation. Studia Logica 67, 2, 243–269.10.1023/A:1010551204574CrossRefGoogle Scholar
Bishop, B. and Fischer, F. 2008. IRIS - integrated rule inference system. In Proc. Workshop on Advancing Reasoning on the Web: Scalability and Commonsense. Vol. 350. CEUR Workshop Proceedings.Google Scholar
Bossi, A., Cocco, N. and Etalle, S. 1992. Transforming normal programs by replacement. In Proc. Meta-Programming in Logic, 3rd International Workshop. Lecture Notes in Computer Science, vol. 649. Springer, 265–279.Google Scholar
Brass, S. and Stephan, H. 2017. Pipelined bottom-up evaluation of Datalog programs: The push method. In Perspectives of System Informatics - 11th International Andrei P. Ershov Informatics Conference, PSI 2017, Petrenko, A. K. and Voronkov, A., Eds. Lecture Notes in Computer Science, vol. 10742. Springer, 43–58.Google Scholar
Brewka, G. 1996. Well-founded semantics for extended logic programs with dynamic preferences. Journal of Artificial Intelligence Research 4, 19–36.Google Scholar
Brewka, G. 2001. On the relationship between defeasible logic and well-founded semantics. In LPNMR. 121–132.10.1007/3-540-45402-0_9CrossRefGoogle Scholar
Calimeri, F., Fuscà, D., Perri, S., and Zangari, J. 2017. I-DLV: the new intelligent grounder of DLV. Intelligenza Artificiale 11, 1, 5–20.CrossRefGoogle Scholar
Carral, D., Dragoste, I., González, L., Jacobs, C. J. H., Krötzsch, M. and Urbani, J. 2019. Vlog: A rule engine for knowledge graphs. In The Semantic Web - ISWC 2019 - 18th International Semantic Web Conference, Part II, Ghidini, C., Hartig, O., Maleshkova, M., Svátek, V., Cruz, I. F., Hogan, A., Song, J., Lefrançois, M., and Gandon, F., Eds. Lecture Notes in Computer Science, vol. 11779. Springer, 19–35.Google Scholar
Cat, B. D., Bogaerts, B., Bruynooghe, M., Janssens, G. and Denecker, M. 2018. Predicate logic as a modeling language: the IDP system. In Declarative Logic Programming: Theory, Systems, and Applications, 279–323.Google Scholar
Chen, W. and Warren, D. S. 1996. Tabled evaluation with delaying for general logic programs. Journal of the ACM 43, 1, 20–74.10.1145/227595.227597CrossRefGoogle Scholar
Chin, B., von Dincklage, D., Ercegovac, V., Hawkins, P., Miller, M. S., Och, F. J., Olston, C. and Pereira, F. 2015. Yedalog: Exploring knowledge at scale. In 1st Summit on Advances in Programming Languages, SNAPL 2015, May 3-6, 2015, Asilomar, California, USA, Ball, T., Bodík, R., Krishnamurthi, S., Lerner, B. S. and Morrisett, G., Eds. LIPIcs, vol. 32. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 63–78.Google Scholar
Cognitect. What is datomic cloud? https://docs.datomic.com/cloud/index.html. Accessed 8/2/2020.Google Scholar
Condie, T., Das, A., Interlandi, M., Shkapsky, A., Yang, M. and Zaniolo, C. 2018 . Scaling-up reasoning and advanced analytics on bigdata. Theory and Practice of Logic Programming 18, 5–6, 806–845.10.1017/S1471068418000418CrossRefGoogle Scholar
Costa, V. S., Rocha, R. and Damas, L. 2012. The YAP Prolog system. Theory and Practice of Logic Programming 12, 1–2, 5–34.10.1017/S1471068411000512CrossRefGoogle Scholar
Covington, M., Nute, D. and Vellino, A. 1997. Prolog Programming in Depth. Prentice-Hall.Google Scholar
Dean, J. and Ghemawat, S. 2004. MapReduce: Simplified data processing on large clusters. In 6th Symposium on Operating System Design and Implementation (OSDI). USENIX Association, Berkeley, CA, USA, 10–10.Google Scholar
Dung, P. M. 1995. On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77, 2, 321–358.10.1016/0004-3702(94)00041-XCrossRefGoogle Scholar
Eisner, J. and Filardo, N. W. 2010. Dyna: Extending Datalog for modern AI. In Datalog Reloaded. 181–220.10.1007/978-3-642-24206-9_11CrossRefGoogle Scholar
Eiter, T., Leone, N. and Saccà, D. 1997. On the partial semantics for disjunctive deductive databases. Annals of Mathematics and Artificial Intelligence 19, 1–2, 59–96.CrossRefGoogle Scholar
Fan, Z., Zhu, J., Zhang, Z., Albarghouthi, A., Koutris, P. and Patel, J. M. 2019. Scaling-up in-memory Datalog processing: Observations and techniques. PVLDB 12, 6, 695–708.Google Scholar
Filardo, N. W. 2017. Dyna 2: Towards a general weighted logic language. Ph.D. thesis, Johns Hopkins University.Google Scholar
Fitting, M. 1985. A Kripke-Kleene semantics for logic programs. Journal of Logical Programming 2, 4, 295–312.10.1016/S0743-1066(85)80005-4CrossRefGoogle Scholar
Gandhe, M., Finin, T. and Grosof, B. 2002. SweetJess: Translating DamlRuleML to Jess. In International Workshop on Rule Markup Languages for Business Rules on the Semantic Web in conjunction with ISWC2002. Sardinia, Italy.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2019. Multi-shot ASP solving with clingo. Theory and Practice of Logic Programming 19, 1, 27–82.CrossRefGoogle Scholar
Gebser, M., Kaminski, R., König, A. and Schaub, T. 2011. Advances in gringo series 3. In Logic Programming and Nonmonotonic Reasoning - 11th International Conference, LPNMR, 345–351.Google Scholar
Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In Proc. JICSLP, 1070–1080.Google Scholar
Governatori, G. and Maher, M. J. 2017. Annotated defeasible logic. Theory and Practice of Logic Programming 17, 5–6, 819–836.10.1017/S1471068417000266CrossRefGoogle Scholar
Governatori, G., Maher, M. J., Antoniou, G. and Billington, D. 2004. Argumentation semantics for defeasible logic. Journal of Logical Computing 14, 5, 675–702.CrossRefGoogle Scholar
Grosof, B. and Kifer, M. 2013. Rulelog: Syntax and semantics. http://ruleml.org/rif/rulelog/spec/Rulelog.html. Accessed: April 2015.Google Scholar
Grosof, B. N. 1997. Prioritized conflict handling for logic programs. In ILPS. 197–211.Google Scholar
Hoder, K., Bjørner, N. and de Moura, L. M. 2011. μZ- an efficient engine for fixed points with constraints. In Computer Aided Verification - 23rd International Conference, CAV. 457–462.Google Scholar
Jaffar, J. and Maher, M. J. 1994. Constraint logic programming: A survey. The Journal of Logic Programming 19 & 20, 503–582.Google Scholar
Jordan, H., Scholz, B. and Subotic, P. 2016. Soufflé: On synthesis of program analyzers. In Computer Aided Verification. 422–430.10.1007/978-3-319-41540-6_23CrossRefGoogle Scholar
Kakas, A. C. and Mancarella, P. 1991. Negation as stable hypotheses. In Logic Programming and Non-monotonic Reasoning, Proceedings of the First International Workshop, 275–288.Google Scholar
Kaminski, R. 2020. personal communication.Google Scholar
Kifer, M., Yang, G., Wan, H. and Zhao, C. 2018. Flora-2 documentation. http://flora.sourceforge.net/documentation.html. Accessed 14/4/2020.Google Scholar
Kunen, K. 1987. Negation in logic programming. Journal of Logical Programming 4, 4, 289–308.10.1016/0743-1066(87)90007-0CrossRefGoogle Scholar
Kunen, K. 1989. Signed data dependencies in logic programs. Journal of Logical Programming 7, 3, 231–245.10.1016/0743-1066(89)90022-8CrossRefGoogle Scholar
Lam, H. and Governatori, G. 2009. The making of SPINdle. In Rule Interchange and Applications, International Symposium, RuleML, Proceedings. 315–322.Google Scholar
Madsen, M. and Lhoták, O. 2020. Fixpoints for the masses: programming with first-class datalog constraints. Proceedings of the ACM on Programming Languages 4, OOPSLA, 125:1–125:28.Google Scholar
Madsen, M., Yee, M. and Lhoták, O. 2016. From Datalog to Flix: a declarative language for fixed points on lattices. In Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation, PLDI 2016, Krintz, C. and Berger, E., Eds. ACM, 194–208.Google Scholar
Maher, M. J. 1988. Correctness of a logic program transformation system. Tech. rep., IBM T.J. Watson Research Center.Google Scholar
Maher, M. J. 1990. Reasoning about stable models (and other unstable semantics). Tech. rep.Google Scholar
Maher, M. J. 1993. A tranformation system for deductive databases modules with perfect model semantics. Theoretical Computer Science 110, 2, 377–403.CrossRefGoogle Scholar
Maher, M. J. 2002. A model-theoretic semantics for defeasible logic. In Paraconsistent Computational Logic, Decker, H., Villadsen, J., and Waragai, T., Eds. Datalogiske Skrifter, vol. 95. Roskilde University, Roskilde, Denmark, 67–80.Google Scholar
Maher, M. J. 2014. Comparing defeasible logics. In 21st European Conference on Artificial Intelligence, 585–590.Google Scholar
Maher, M. J. 2017. Relating concrete defeasible reasoning formalisms and abstract argumentation. Fundamenta Informaticae 155, 3, 233–260.10.3233/FI-2017-1584CrossRefGoogle Scholar
Maher, M. J. 2021. On signings and the well-founded semantics. Theory and Practice of Logic Programming accepted for publication.CrossRefGoogle Scholar
Maher, M. J. and Governatori, G. 1999. A semantic decomposition of defeasible logics. In AAAI/IAAI. AAAI Press, 299–305.Google Scholar
Maher, M. J., Rock, A., Antoniou, G., Billington, D. and Miller, T. 2001. Efficient defeasible reasoning systems. International Journal on Artificial Intelligence Tools 10, 4, 483–501.10.1142/S0218213001000623CrossRefGoogle Scholar
Maher, M. J., Tachmazidis, I., Antoniou, G., Wade, S. and Cheng, L. 2020. Rethinking defeasible reasoning: A scalable approach. Theory and Practice of Logic Programming. 20, 4, 552–586.10.1017/S1471068420000010CrossRefGoogle Scholar
Maier, F. 2013. Interdefinability of defeasible logic and logic programming under the well-founded semantics. Theory and Practice of Logic Programming 13, 1, 107–142.CrossRefGoogle Scholar
Maier, F. and Nute, D. 2006. Ambiguity propagating defeasible logic and the well-founded semantics. In JELIA, Fisher, M., van der Hoek, W., Konev, B., and Lisitsa, A., Eds. Lecture Notes in Computer Science, vol. 4160. Springer, 306–318.Google Scholar
Maier, F. and Nute, D. 2010. Well-founded semantics for defeasible logic. Synthese 176, 2, 243–274.10.1007/s11229-009-9492-1CrossRefGoogle Scholar
Martinez-Angeles, C. A., de Castro Dutra, I., Costa, V. S., and Buenabad-Chávez, J. 2013. A Datalog engine for GPUs. In Declarative Programming and Knowledge Management. 152–168.CrossRefGoogle Scholar
Marz, N. 2013. Cascalog. https://www.cascading.org/projects/cascalog/. Accessed: April 2020.Google Scholar
Nguyen, H. D., Sakama, C., Sato, T., and Inoue, K. 2018. Computing logic programming semantics in linear algebra. In Multi-disciplinary Trends in Artificial Intelligence - 12th International Conference, MIWAI, 32–48.Google Scholar
Niemelä, I. and Simons, P. 1997. Smodels - An implementation of the stable model and well-founded semantics for normal LP. In Logic Programming and Nonmonotonic Reasoning, 4th International Conference, LPNMR’97, Dix, J., Furbach, U., and Nerode, A., Eds. Lecture Notes in Computer Science, vol. 1265. Springer, 421–430.Google Scholar
Nute, D. 1993. Defeasible Prolog. In Proc. AAAI Fall Symposium on Automated Deduction in Nonstandard Logics, 105–112.Google Scholar
Przymusinski, T. C. 1990. The well-founded semantics coincides with the three-valued stable semantics. Fundamenta Informaticae 13, 4, 445–463.CrossRefGoogle Scholar
Sato, T. 2017. A linear algebraic approach to Datalog evaluation. Theory and Practice of Logic Programming 17, 3, 244–265.CrossRefGoogle Scholar
Sato, T., Sakama, C. and Inoue, K. 2020. From 3-valued semantics to supported model computation for logic programs in vector spaces. In Proceedings of the 12th International Conference on Agents and Artificial Intelligence, ICAART 2020. 758–765.Google Scholar
Seo, J., Guo, S. and Lam, M. S. 2015. Socialite: An efficient graph query language based on Datalog. IEEE Transactions on Knowledge and Data Engineering 27, 7, 1824–1837.CrossRefGoogle Scholar
Swift, T. and Warren, D. S. 2012. XSB: Extending Prolog with tabled logic programming. Theory and Practice of Logic Programming 12, 1-2, 157–187.10.1017/S1471068411000500CrossRefGoogle Scholar
Swift, T., Warren, D. S., et al. 2017. The XSB System, Version 3.8.x, Volume 1: Programmers Manual. Tech. rep.Google Scholar
Tachmazidis, I. and Antoniou, G. 2013. Computing the stratified semantics of logic programs over big data through mass parallelization. In RuleML. Lecture Notes in Computer Science, vol. 8035. Springer, 188–202.Google Scholar
Tachmazidis, I., Antoniou, G. and Faber, W. 2014. Efficient computation of the well-founded semantics over big data. Theory and Practice of Logic Programming 14, 4-5, 445–459.10.1017/S1471068414000131CrossRefGoogle Scholar
Tachmazidis, I., Antoniou, G., Flouris, G., Kotoulas, S., and McCluskey, L. 2012. Large-scale parallel stratified defeasible reasoning. In ECAI 2012 - 20th European Conference on Artificial Intelligence, 738–743.Google Scholar
Tachmazidis, I., Cheng, L., Kotoulas, S., Antoniou, G. and Ward, T. E. 2014. Massively parallel reasoning under the well-founded semantics using X10. In 26th IEEE International Conference on Tools with Artificial Intelligence, ICTAI 2014. IEEE Computer Society, 162–169.Google Scholar
Tamaki, H. and Sato, T. 1984. Unfold/fold transformation of logic programs. In Proc. ICLP, 127–138.Google Scholar
Van Gelder, A., Ross, K. A. and Schlipf, J. S. 1991. The well-founded semantics for general logic programs. J. ACM 38, 3, 620–650.CrossRefGoogle Scholar
Wan, H., Grosof, B. N., Kifer, M., Fodor, P. and Liang, S. 2009. Logic programming with defaults and argumentation theories. In ICLP, Hill, P. M. and Warren, D. S., Eds. Lecture Notes in Computer Science, vol. 5649. Springer, 432–448.Google Scholar
Wang, J., Balazinska, M., and Halperin, D. 2015. Asynchronous and fault-tolerant recursive Datalog evaluation in shared-nothing engines. Proceedings of the VLDB Endowment 8, 12, 1542–1553.10.14778/2824032.2824052CrossRefGoogle Scholar
Wang, K., Hussain, A., Zuo, Z., Xu, G. H. and Sani, A. A. 2017. Graspan: A single-machine disk-based graph system for interprocedural static analyses of large-scale systems code. In Proceedings of the Twenty-Second International Conference on Architectural Support for Programming Languages and Operating Systems, ASPLOS, 389–404.Google Scholar
Wenzel, M. and Brass, S. 2019. Declarative programming for microcontrollers - Datalog on Arduino. In Declarative Programming and Knowledge Management - Conference on Declarative Programming, DECLARE 2019, Unifying INAP, WLP, and WFLP, Hofstedt, P., Abreu, S., John, U., Kuchen, H. and Seipel, D., Eds. Lecture Notes in Computer Science, vol. 12057. Springer, 119–138.Google Scholar
Whaley, J., Avots, D., Carbin, M. and Lam, M. S. 2005. Using Datalog with binary decision diagrams for program analysis. In Programming Languages and Systems, Third Asian Symposium, APLAS, 97–118.Google Scholar
Wu, H., Diamos, G. F., Sheard, T., Aref, M., Baxter, S., Garland, M. and Yalamanchili, S. 2014. Red fox: An execution environment for relational query processing on gpus. In 12th Annual IEEE/ACM International Symposium on Code Generation and Optimization, CGO, Kaeli, D. R. and Moseley, T., Eds. ACM, 44.Google Scholar
You, J. and Yuan, L. 1994. A three-valued semantics for deductive databases and logic programs. Journal of Computer and System Sciences 49, 2, 334–361.CrossRefGoogle Scholar