×

zbMATH — the first resource for mathematics

A general approach to reasoning with probabilities. (English) Zbl 1454.68144
Summary: We propose a general scheme for adding probabilistic reasoning capabilities to a wide variety of knowledge representation formalisms and we study its properties. Syntactically, we consider adding probabilities to the formulas of a given base logic. Semantically, we define a probability distribution over the subsets of a knowledge base by taking the probabilities of the formulas into account accordingly. This gives rise to a probabilistic entailment relation that can be used for uncertain reasoning. Our approach is a generalisation of many concrete probabilistic enrichments of existing approaches, such as ProbLog (an approach to probabilistic logic programming) and the constellation approach to abstract argumentation. We analyse general properties of our approach and provide some insights into novel instantiations that have not been investigated yet.
MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
68N17 Logic programming
68T30 Knowledge representation
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bacchus, Fahiem; Grove, Adam J.; Halpern, Joseph Y.; Koller, Daphne, From statistical knowledge bases to degrees of belief, Artif. Intell., 87, 1-2, 75-143 (1996)
[2] Baral, Chitta; Gelfond, Michael; Rushton, Nelson, Probabilistic reasoning with answer sets, (Lifschitz, Vladimir; Niemelä, Ilkka, Logic Programming and Nonmonotonic Reasoning (2004), Springer: Springer Berlin Heidelberg), 21-33 · Zbl 1122.68361
[3] Brachman, Ronald J.; Levesque, Hector J., Knowledge Representation and Reasoning (2004), Morgan Kaufmann Publishers · Zbl 1341.68228
[4] Bratko, Ivan, Prolog Programming for Artificial Intelligence (2001), Addison Wesley · Zbl 0599.68007
[5] Brewka, Gerhard; Ellmauthaler, Stefan; Strass, Hannes; Wallner, Johannes Peter; Woltran, Stefan, Abstract dialectical frameworks revisited, (Proceedings of the 23rd International Joint Conference on Artificial Intelligence (2013)), 803-809
[6] Cayrol, C.; Lagasquie-Schiex, M. C., On the acceptability of arguments in bipolar argumentation frameworks, (Godo, Lluís, Symbolic and Quantitative Approaches to Reasoning with Uncertainty (2005), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 378-389 · Zbl 1122.68639
[7] Cerutti, Federico; Thimm, Matthias, A general approach to reasoning with probabilities (extended abstract), (Proceedings of the 16th International Conference on Principles of Knowledge Representation and Reasoning (KR’19) (October 2018))
[8] Cerutti, Federico; Thimm, Matthias, Probabilistic augmentations for knowledge representation formalisms, (Proceedings of the Workshop on Hybrid Reasoning and Learning (HRL’18) (October 2018))
[9] Dalvi, Nilesh; Suciu, Dan, Efficient query evaluation on probabilistic databases, VLDB J., 16, 4, 523-544 (2007)
[10] De Raedt, Luc; Kersting, Kristian; Natarajan, Sriraam; Poole, David, Statistical Relational Artificial Intelligence: Logic, Probability, and Computation. Synthesis Lectures on Artificial Intelligence and Machine Learning (2016), Morgan & Claypool Publishers · Zbl 1352.68005
[12] De Raedt, Luc; Kimmig, Angelika; Gutmann, Bernd; Kersting, Kristian; Santos Costa, Vitor; Toivonen, Hannu, Probabilistic Inductive Querying Using Problog (June 2009), Department of Computer Science, Katholieke Universiteit Leuven: Department of Computer Science, Katholieke Universiteit Leuven Belgium, Technical Report CW 552
[13] Di Pierro, Alessandra; Wiklicky, Herbert, Probabilistic concurrent constraint programming: towards a fully abstract model, (Brim, Luboš; Gruska, Jozef; Zlatuška, Jiří, Mathematical Foundations of Computer Science 1998 (1998), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 446-455 · Zbl 0952.68090
[14] Domingos, Pedro; Lowd, Daniel, Markov Logic: An Interface Layer for Artificial Intelligence. Synthesis Lectures on Artificial Intelligence and Machine Learning (2009), Morgan and Claypool: Morgan and Claypool San Rafael, CA · Zbl 1202.68403
[15] Dragiev, Stanislav; Russo, Alessandra; Broda, Krysia; Law, Mark; Turliuc, Calin-Rares, An abductive-inductive algorithm for probabilistic inductive logic programming, (Proceedings of the 26th International Conference on Inductive Logic Programming (Short papers) (2016)), 20-26
[16] Dung, Phan Minh, On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games, Artif. Intell., 77, 2, 321-357 (1995) · Zbl 1013.68556
[17] Fagin, Ronald; Halpern, Joseph Y., Reasoning about knowledge and probability, J. ACM, 41, 2, 340-367 (1994) · Zbl 0806.68098
[18] Fazzinga, Bettina; Flesca, Sergio; Furfaro, Filippo, Probabilistic bipolar abstract argumentation frameworks: complexity results, (IJCAI (2018)), 1803-1809
[19] Fazzinga, Bettina; Flesca, Sergio; Furfaro, Filippo, Complexity of fundamental problems in probabilistic abstract argumentation: beyond independence, Artif. Intell., 268, 1-29 (2019) · Zbl 07099175
[21] Fuhr, Norbert, Probabilistic datalog: implementing logical information retrieval for advanced applications, J. Assoc. Inf. Sci. Technol., 51, 2, 95-110 (2000)
[22] Gebser, Martin; Kaminski, Roland; Kaufmann, Benjamin; Schaub, Torsten, Answer Set Solving in Practice (2012), Morgan & Claypool Publishers · Zbl 1251.68060
[23] Gelfond, Michael; Leone, Nicola, Logic programming and knowledge representation – the A-Prolog perspective, Artif. Intell., 138, 1-2, 3-38 (2002) · Zbl 0995.68022
[24] Gelfond, Michael; Lifschitz, Vladimir, Classical negation in logic programs and disjunctive databases, New Gener. Comput., 9, 3/4, 365-386 (1991) · Zbl 0735.68012
[25] Gupta, Vineet; Jagadeesan, Radha; Saraswat, Vijay, Probabilistic concurrent constraint programming, (Mazurkiewicz, Antoni; Winkowski, Józef, CONCUR ’97: Concurrency Theory (1997), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg), 243-257
[26] Hájek, Petr, Metamathematics of Fuzzy Logic (1998), Kluwer: Kluwer Dordrecht · Zbl 0937.03030
[28] Duy Hung, Nguyen, The distribution semantics of extended argumentation, (Proceedings of the 18th International Symposium on Knowledge and Systems Sciences (2017)), 197-211
[29] Hunter, Anthony, Some foundations for probabilistic abstract argumentation, (Proceedings of the 4th International Conference on Computational Models of Argument (2012)), 117-128
[30] Hunter, Anthony, Probabilistic qualification of attack in abstract argumentation, Int. J. Approx. Reason., 55, 2, 607-638 (2014) · Zbl 1316.68153
[31] Kohlas, Jürg, Probabilistic argumentation systems: a new way to combine logic with probability, J. Appl. Log., 1, 3, 225-253 (2003), Combining Probability and Logic · Zbl 1037.03018
[32] Kohlas, Jürg; Anrig, Bernhard; Haenni, Rolf; Monney, Paul-André, Model-based diagnostics and probabilistic assumption-based reasoning, Artif. Intell., 104, 1-2, 71-106 (September 1998)
[33] Kohlas, Jürg; Monney, Paul-André, Probabilistic Assumption-Based Reasoning, 82-135 (1995), Springer Berlin Heidelberg: Springer Berlin Heidelberg Berlin, Heidelberg
[34] Kowalski, Robert A., The early years of logic programming, Commun. ACM, 31, 1, 38-43 (1988)
[35] Li, Hengfei; Oren, Nir; Norman, Timothy J., Probabilistic argumentation frameworks, (Proceedings of the First International Workshop on the Theory and Applications of Formal Argumentation (2011)), 1-16
[37] Lukasiewicz, Thomas, Probabilistic logic programming, (ECAI (1998)), 388-392
[38] Lukasiewicz, Thomas, Local probabilistic deduction from taxonomic and probabilistic knowledge-bases over conjunctive events, Int. J. Approx. Reason., 21, 1, 23-61 (1999) · Zbl 0961.68135
[39] Mantadelis, Theofrastos; Janssens, Gerda, Dedicated tabling for a probabilistic setting, (Hermenegildo, Manuel; Schaub, Torsten, Technical Communications of the 26th International Conference on Logic Programming. Technical Communications of the 26th International Conference on Logic Programming, Leibniz International Proceedings in Informatics (LIPIcs), vol. 7 (2010), Dagstuhl: Dagstuhl Germany), 124-133, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik · Zbl 1237.68190
[40] Modgil, Sanjay; Prakken, Henry, The ASPIC+ framework for structured argumentation: a tutorial, Argum. Comput., 5, 31-62 (2014)
[41] Nilsson, Nils J., Probabilistic logic, Artif. Intell., 28, 1, 71-87 (1986) · Zbl 0589.03007
[42] Paris, Jeff B., The Uncertain Reasoner’s Companion - A Mathematical Perspective (1994), Cambridge University Press · Zbl 0838.68104
[43] Pearl, Judea, Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference (1988), Springer-Verlag · Zbl 0746.68089
[44] Polberg, Sylwia; Doder, Dragan, Probabilistic abstract dialectical frameworks, (Proceedings of the 14th European Conference on Logics in Artificial Intelligence (2014)), 591-599 · Zbl 1343.68228
[45] Poole, David, Representing diagnostic knowledge for probabilistic horn abduction, (Proceedings of the 12th International Joint Conference on Artificial Intelligence - Volume 2. Proceedings of the 12th International Joint Conference on Artificial Intelligence - Volume 2, IJCAI’91 (1991), Morgan Kaufmann Publishers Inc.: Morgan Kaufmann Publishers Inc. San Francisco, CA, USA), 1129-1135 · Zbl 0749.68086
[46] Poole, David, Probabilistic horn abduction and bayesian networks, Artif. Intell., 64, 1, 81-129 (1993) · Zbl 0792.68176
[47] Poole, David, The independent choice logic and beyond, (Luc De Raedt; Frasconi, Paolo; Kersting, Kristian; Muggleton, Stephen, Probabilistic Inductive Logic Programming: Theory and Application. Probabilistic Inductive Logic Programming: Theory and Application, Lecture Notes in Artificial Intelligence, vol. 4911 (2008), Springer) · Zbl 1137.68596
[48] Poole, David, Probabilistic programming languages: independent choices and deterministic systems, (Heuristics, Probability and Causality: A Tribute to Judea Pearl (2010), College Publications) · Zbl 1216.68070
[49] Potyka, Nico; Thimm, Matthias, Consolidation of probabilistic knowledge bases by inconsistency minimization, (Proceedings of the 21st European Conference on Artificial Intelligence (2014)), 729-734 · Zbl 1366.68316
[50] Proietti, Carlo, Polarization and bipolar probabilistic argumentation frameworks, (AÎ 3@ AI* IA (2017)), 22-27
[51] Reiter, Raymond, A logic for default reasoning, Artif. Intell., 13, 81-132 (1980) · Zbl 0435.68069
[52] Richardson, Matthew; Domingos, Pedro, Markov logic networks, Mach. Learn., 62, 1-2, 107-136 (2006)
[53] Rienstra, Tjitze, Towards a probabilistic Dung-style argumentation system, (Proceedings of the First International Conference on Agreement Technologies (2012)), 138-152
[54] Saraswat, Vijay A.; Rinard, Martin, Concurrent constraint programming, (Proceedings of the 17th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. Proceedings of the 17th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL ’90 (1990), ACM: ACM New York, NY, USA), 232-245
[55] Sato, Taisuke, A statistical learning method for logic programs with distribution semantics, (Proceedings of the 12th International Conference on Logic Programming (1995)), 715-729
[56] Shafer, Glenn, A Mathematical Theory of Evidence (1976), Princeton University Press · Zbl 0359.62002
[57] Suciu, Dan; Olteanu, Dan; Re, Christopher; Koch, Christoph, Probabilistic Databases (2011), Morgan & Claypool Publishers · Zbl 1237.68012
[58] Wilson, Nic, How much do you believe?, Int. J. Approx. Reason., 6, 3, 345-365 (May 1992)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.