Abstract
We show how to encode, retrieve and process complex structures equivalent to First-Order Logic (FOL) formulae, with Artificial Neural Networks (ANNs) designed for energy-minimization. The solution constitutes a binding mechanism that uses a neural Working Memory (WM) and a long-term synaptic memory (LTM) that can store both procedural and declarative FOL-like Knowledge-Base (KB). Complex structures stored in LTM are retrieved into the WM only upon need, where they are further processed. The power of our binding mechanism is demonstrated on unification problems: as neurons are dynamically allocated from a pool, most generally unified structures emerge at equilibrium. The network’s size is O(n·k), where n is the size of the retrieved FOL structures and k is the size of the KB. The mechanism is fault-tolerant, as no fatal failures occur when random units fail. The paradigm can be used in a variety of applications, such as language processing, reasoning and planning.
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References
Ballard, D.H.: Parallel logical inference and energy minimization. In: Proceedings of the AAAI National Conference on Artificial Intelligence, pp. 203–208 (1986)
Barrett, L., Feldman, J.A., Dermed, M.L.: A (somewhat) new solution to the binding problem. Neural Computation 20, 2361–2367 (2008)
Browne, A., Sun, R.: Connectionist variable binding. Springer, Heidelberg (2000)
d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: Neuro-Symbolic Cognitive Reasoning, Cognitive Technologies. Springer (2008)
Feldman, J.: The Binding Problem(s) (2010), http://www.computational-logic.org/content/events/iccl-ss-2010/slides/feldman/papers/Binding8.pdf
Fodor, J.A., Phylyshyn, Z.W.: Connectionism and cognitive architecture: A critical analysis. In: Pinker, Mehler (eds.) Connectionism and Symbols, pp.3–71. MIT Press (1988)
Hölldobler, S.: A Structured Connectionist Unification Algorithm. In: Proceedings of the Eighth National Conference on Artificial Intelligence, vol. 1 (1990)
Hölldobler, S., Kurfess, F.: CHCL-A Connectionist Inference System. In: Fronhöfer, B., Wrightson, G. (eds.) Dagstuhl Seminar 1990. LNCS (LNAI), vol. 590, pp. 318–342. Springer, Heidelberg (1992)
Jackendoff, R.: Foundations of Language: Brain, Meaning, Grammar, Evolution. Oxford University Press (2002)
Komendantskaya, E.: Unification neural networks: unification by error-correction learning. Logic Jnl IGPL (2010)
Paterson, M., Wegman, M.: Linear unification. J. Comput. Syst. Sci. 16(2), 158–167 (1978)
Pinkas, G.: Reasoning, non-monotonicity and learning in connectionist networks that capture propositional knowledge. Artificial Intelligence 77, 203–247 (1995)
Pinkas, G.: Symmetric neural networks and logic satisfiability. Neural Comp. 3(2) (1991)
Pinkas, G.: Constructing proofs symmetric networks. In: NIPS-4, pp. 217–224 (1992)
Plate, T.: Holographic Reduced Representations. IEEE Trans. Neural Network 6(3) (2003)
Shastri, L., Ajjanagadde, V.: From associations to systematic reasoning: A connectionist representation of rules, variables and bindings. BBS 16(3), 417–494 (1993)
Lima, P.M.V.: Resolution-Based Inference on Artificial Neural Networks. Ph.D. Thesis, Department of Computing. Imperial College London, UK (2000)
Stolke, A.: Unification as Constraint Satisfaction in Structured Connectionist Networks. Neural Computation 1(4), 558–566 (1989)
Van der Velde, F., Kamps, M.: Neural blaclboard architectures of combinatorial structures and cognition. Behav. Brain Sci. 29, 1–72 (2006)
Bader, S., Hitzler, S., Holdobler, S.: Connectionist model generation: A first-order approach. Neurocomputing 71, 2420–2432 (2008)
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Pinkas, G., Lima, P., Cohen, S. (2012). A Dynamic Binding Mechanism for Retrieving and Unifying Complex Predicate-Logic Knowledge. In: Villa, A.E.P., Duch, W., Érdi, P., Masulli, F., Palm, G. (eds) Artificial Neural Networks and Machine Learning – ICANN 2012. ICANN 2012. Lecture Notes in Computer Science, vol 7552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33269-2_61
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DOI: https://doi.org/10.1007/978-3-642-33269-2_61
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