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Erschienen in:
Understanding Characteristics of Evolved Instances for State-of-the-Art Inexact TSP Solvers with Maximum Performance Difference Kapitel lesen Erstes Kapitel lesen

2016 | OriginalPaper | Buchkapitel

Learning and Reasoning with Logic Tensor Networks

verfasst von : Luciano Serafini, Artur S. d’Avila Garcez

Erschienen in: AI*IA 2016 Advances in Artificial Intelligence

Verlag: Springer International Publishing

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Abstract

The paper introduces real logic: a framework that seamlessly integrates logical deductive reasoning with efficient, data-driven relational learning. Real logic is based on full first order language. Terms are interpreted in n-dimensional feature vectors, while predicates are interpreted in fuzzy sets. In real logic it is possible to formally define the following two tasks: (i) learning from data in presence of logical constraints, and (ii) reasoning on formulas exploiting concrete data. We implement real logic in an deep learning architecture, called logic tensor networks, based on Google’s \(\textsc {TensorFlow}^{\tiny {\text {TM}}}\) primitives. The paper concludes with experiments on a simple but representative example of knowledge completion.

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Vorheriges Kapitel On-line Learning on Temporal Manifolds
Nächstes Kapitel Probabilistic Logical Inference on the Web
Fußnoten
1
In logic, the term “grounding” indicates the operation of replacing the variables of a term/formula with constants, or terms that do not contains other variables. To avoid confusion, we use the synonym “instantiation” for this sense.
 
3
Normally, a probabilistic approach is taken to solve this problem, and one that requires instantiating all clauses to remove variables, essentially turning the problem into a propositional one; ltn takes a different approach.
 
4
Notice how no grounding is provided about the signature of the knowledge-base.
 
5
A smoth factor \(\lambda ||\mathbf {\Omega }||^2_2\) is added to the loss to limit the size of parameters.
 
6
\(\mu (a,b) = \min (1,a+b)\).
 
Literatur
1.
Bengio, Y.: Learning deep architectures for AI. Found. Trends Mach. Learn. 2, 1–127 (2009)CrossRefMATH
2.
Silver, D., Huang, A., Maddison, C.J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., Dieleman, S., Grewe, D., Nham, J., Kalchbrenner, N., Sutskever, I., Lillicrap, T., Leach, M., Kavukcuoglu, K., Graepel, T., Hassabis, D.: Mastering the game of go with deep neural networks and tree search. Nature 529, 484–503 (2016)CrossRef
3.
Kephart, J.O., Chess, D.M.: The vision of autonomic computing. Computer 36, 41–50 (2003)CrossRef
4.
Kiela, D., Bottou, L.: Learning image embeddings using convolutional neural networks for improved multi-modal semantics. In: Proceedings of EMNLP 2014 (2014)
5.
Socher, R., Chen, D., Manning, C.D., Ng, A.: Reasoning with neural tensor networks for knowledge base completion. In: Advances in Neural Information Processing Systems, pp. 926–934 (2013)
6.
Guha, R.: Towards a model theory for distributed representations. In: 2015 AAAI Spring Symposium Series (2015)
7.
8.
d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: Neural-Symbolic Cognitive Reasoning. Cognitive Technologies. Springer, Heidelberg (2009)MATH
9.
10.
Barrett, L., Feldman, J., MacDermed, L.: A (somewhat) new solution to the variable binding problem. Neural Comput. 20, 2361–2378 (2008)CrossRefMATH
11.
Bergmann, M.: An Introduction to Many-Valued and Fuzzy Logic: Semantics, Algebras, and Derivation Systems. Cambridge University Press, New York (2008)CrossRefMATH
12.
13.
d’Avila Garcez, A.S., Gori, M., Hitzler, P., Lamb, L.C.: Neural-symbolic learning and reasoning (dagstuhl seminar 14381). Dagstuhl Rep. 4, 50–84 (2014)
14.
McCallum, A., Gabrilovich, E., Guha, R., Murphy, K. (eds.): Knowledge representation and reasoning: integrating symbolic and neural approaches. In: AAAI Spring Symposium, Stanford University, CA, USA (2015)
15.
Besold, T.R., d’Avila Garcez, A., Marcus, G.F., Miikulainen, R. (eds.): Cognitive computation: integrating neural and symbolic approaches. In: Workshop at NIPS 2015, Montreal, Canada, CEUR-WS 1583, April 2016
16.
Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press, New York (2004)CrossRefMATH
17.
Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022 (2003)MATH
18.
Brys, T., Drugan, M.M., Bosman, P.A., De Cock, M., Nowé, A.: Solving satisfiability in fuzzy logics by mixing CMA-ES. In: Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation, GECCO 2013, pp. 1125–1132. ACM, New York (2013)
19.
Richardson, M., Domingos, P.: Markov logic networks. Mach. Learn. 62, 107–136 (2006)CrossRef
20.
Tieleman, T., Hinton, G.: Lecture 6.5 - RMSProp, COURSERA: Neural networks for machine learning. Technical report (2012)
21.
Wang, J., Domingos, P.M.: Hybrid markov logic networks. In: AAAI, pp. 1106–1111 (2008)
22.
Nath, A., Domingos, P.M.: Learning relational sum-product networks. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, January 25–30, 2015, Austin, Texas, USA, pp. 2878–2886 (2015)
23.
Kosko, B.: Neural Networks and Fuzzy Systems: A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall Inc., Upper Saddle River (1992)MATH
24.
Milch, B., Marthi, B., Russell, S.J., Sontag, D., Ong, D.L., Kolobov, A.: BLOG: probabilistic models with unknown objects. In: IJCAI 2005, pp. 1352–1359 (2005)
25.
Raedt, L.D., Kersting, K., Natarajan, S., Poole, D.: Statistical Relational Artificial Intelligence: Logic, Probability, and Computation. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool, San Rafael (2016)MATH
26.
Muggleton, S.H., Lin, D., Tamaddoni-Nezhad, A.: Meta-interpretive learning of higher-order dyadic datalog: predicate invention revisited. Mach. Learn. 100, 49–73 (2015)MathSciNetCrossRefMATH
27.
França, M.V.M., Zaverucha, G., d’Avila Garcez, A.S.: Fast relational learning using bottom clause propositionalization with artificial neural networks. Mach. Learn. 94, 81–104 (2014)MathSciNetCrossRef
Metadaten
Titel
Learning and Reasoning with Logic Tensor Networks
verfasst von
Luciano Serafini
Artur S. d’Avila Garcez
Copyright-Jahr
2016
Buch
AI*IA 2016 Advances in Artificial Intelligence

Print ISBN: 978-3-319-49129-5

Electronic ISBN: 978-3-319-49130-1

Copyright-Jahr: 2016

DOI
https://doi.org/10.1007/978-3-319-49130-1_25