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Fuzzy non-horn knowledge bases: calculi, models, inference
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 176-190 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper investigates inference in knowledge bases with fuzzy fuzzy non-Horn facts and rules. Sequent calculi with one structural, one logical rule, and non-logical axioms representing knowledge base rules and facts serve as a proof theory for these knowledge bases. These knowledge bases are also characterized by constrained real-valued models which are applicable to a variety of truth functions. Inference for fuzzy non-Horn knowledge bases is done by applying a variant of ordered resolution, transforming resolution refuations into sequent calculus derivations, building symbolic expressions from the derivations, and evaluating the symbolic expressions. 
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A. Sakharov. Fuzzy non-horn knowledge bases: calculi, models, inference. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXIV, Tome 517 (2022), pp. 176-190. http://geodesic.mathdoc.fr/item/ZNSL_2022_517_a10/

[1] B. Leo, G. Harald, “Resolution theorem proving”, Handbook of automated reasoning, Elsevier, 2001, 19–99

[2] Barros Laécio Carvalho de, Bassanezi Rodney Carlos, Lodwick Weldon Alexander, A first course in fuzzy logic, fuzzy dynamical systems, and biomathematics: theory and applications, Springer, 2017 | MR

[3] Ch. Chin-Liang, L. Richard Char-Tung, Symbolic logic and mechanical theorem proving, Academic press, 1973 | MR

[4] Petr C. Hájek, Petr N. Carles, Handbook of Mathematical Fuzzy Logic, College Publ., 1, 2011

[5] D. Honghua Mao Jiayuan, Lin Tian, Wang Chong, Li Lihong, Zhou Denny, “Neural logic machines”, Inter. Conf. Learning Representations, 2019

[6] D. Didier, P. Henri, “Possibilistic Logic-An Overview”, Computational logic, 2014, 197–255

[7] G. Siegfried, A treatise on many-valued logics, Research Studies Press, 2001 | MR

[8] H. Petr, Metamathematics of fuzzy logic, Springer Science Business Media, 2013

[9] H. Jinyung, P. Theodore, “An insect-inspired randomly, weighted neural network with random fourier features for neuro-symbolic relational learning”, Neural-Symbolic Learning and Reasoning, 2021 CEUR-WS.org

[10] T. Ishihara, K. Hayashi, H. Manabe, M. Shimbo, M. Nagata, “Neural tensor networks with diagonal slice matrices”, Proceedings of the 2018 Conf. North American Chapter of the Association for Comput. Linguistics: Human Language Techn., v. 1, 2018, 506–515 | DOI

[11] L. Kovács, A. Voronkov, “First-order theorem proving and Vampire”, International Conference on Computer Aided Verification, Springer, 2013, 1–35 | MR

[12] R. Manhaeve, S. Dumančić, A. Kimmig, Th. Demeester, L. De Raedt, “Neural probabilistic logic programming in DeepProbLog”, Artificial Intelligence, 298 (2021), 103–504 | DOI | MR

[13] W. McCune, Otter 3.3 reference manual and guide, Tecnical report, Argonne National Lab, 2003

[14] S. Negri, J. Von Plato, Structural proof theory, Cambridge University Press, 2001 | MR

[15] L. De Raedt, A. Kimmig, “Probabilistic (logic) programming concepts”, Machine Learning, 100:1 (2015), 5–47 | DOI | MR

[16] R. Riegel, A. Gray, F. Luus, N. Khan, N. Makondo, I. Y. Akhalwaya, H. Qian, R. Fagin, F. Barahona, U. Sharma, Logical neural networks, 2020, arXiv: 2006.13155

[17] S. Russell, P. Norvig, Artificial Intelligence: A Modern Approach, 3rd edition, Prentice Hall Press, 2009

[18] A. Sakharov, “Inference Methods for Evaluable Knowledge Bases”, Software Engineering Application in Informatics, Lecture Notes in Networks and Systems, Springer, 2021, 499–510 | DOI

[19] A. Sakharov, “Calculi and Models for Non-Horn Knowledge Bases Containing Neural and Evaluable Predicates”, Logics for New-Generation AI, College Publications, 2022, 24–35

[20] A. Sakharov, “A Logical Characterization of Evaluable Knowledge Bases”, 14th International Conference on Agents and Artificial Intelligence, 2022, 681–688

[21] A. Sakharov, “Symbolic Inference for Non-Horn Knowledge Bases With Fuzzy Predicates”, Polynomial Computer Algebra, 2022, 86–95

[22] A. Santoro, D. Raposo, David G. Barrett, M. Malinowski, R. Pascanu, P. Battaglia, T. Lillicrap, “A simple neural network module for relational reasoning”, Adv. neural inform. proc. systems, 30 (2017)

[23] L. Serafini, Artur S. d'Avila Garcez, “Logic Tensor Networks: Deep Learning and Logical Reasoning from Data and Knowledge”, Neural-Symbolic Learning and Reasoning, 2016 CEUR-WS.org