Research into the processing of symbolic knowledge by means of connectionist networks aims at systems which combine the declarative nature of logicbased artificial intelligence with the robustness and trainability of artificial neural networks. This endeavour has been addressed quite successfully in the past for propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended beyond propositional logic, it is not obvious at all what neuralsymbolic systems should look like such that they are truly connectionist and allow for a declarative reading at the same time.
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References
McCulloch, W.S., Pitts, W.: A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics 5 (1943) 115-133
Pinkas, G.: Symmetric neural networks and logic satisfiability. Neural Computation 3 (1991) 282-291
McCarthy, J.: Epistemological challanges for connectionism. Behavioural and Brain Sciences 11 (1988) 44 Commentary to [12].
Bader, S., Hitzler, P.: Dimensions of neural-symbolic integration - a struc-tured survey. In: S. Artemov, H. Barringer, A. S. d’Avila Garcez, L. C. Lamb and J. Woods (eds).: We Will Show Them: Essays in Honour of Dov Gabbay, Volume 1. International Federation for Computational Logic, College Publica-tions (2005) 167-194
Ballard, D.H.: Parallel logic inference and energy minimization. In: Proceedings of the AAAI National Conference on Artificial Intelligence. (1986) 203 - 208
Lange, T.E., Dyer, M.G.: High-level inferencing in a connectionist network. Connection Science 1 (1989) 181-217
Shastri, L., Ajjanagadde, V.: From associations to systematic reasoning: A con-nectionist representation of rules, variables and dynamic bindings using tempo-ral synchrony. Behavioural and Brain Sciences 16 (1993) 417-494
Hölldobler, S., Kurfess, F.: CHCL - A connectionist inference system. In Fronhöfer, B., Wrightson, G., eds.: Parallelization in Inference Systems. Springer, LNAI 590 (1992) 318 - 342
Pollack, J.B.: Recursive distributed representations. AIJ 46 (1990) 77-105
Plate, T.A.: Holographic reduced networks. In Giles, C.L., Hanson, S.J., Cowan, J.D., eds.: Advances in Neural Information Processing Systems 5. Morgan Kaufmann (1992)
Elman, J.L.: Structured representations and connectionist models. In: Proceed-ings of the Annual Conference of the Cognitive Science Society. (1989) 17-25
Smolensky, P.: On variable binding and the representation of symbolic struc-tures in connectionist systems. Technical Report CU-CS-355-87, Department of Computer Science & Institute of Cognitive Science, University of Colorado, Boulder, CO 80309-0430 (1987)
Bader, S., Hitzler, P., Hölldobler, S.: The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Arti-ficial Intelligence. Information 9 (2006).
Towell, G.G., Shavlik, J.W.: Extracting refined rules from knowledge-based neural networks. Machine Learning 13 (1993) 71-101
Hölldobler, S., Kalinke, Y.: Towards a massively parallel computational model for logic programming. In: Proceedings ECAI94 Workshop on Combining Sym-bolic and Connectionist Processing, ECCAI (1994) 68-77
Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press (1995)
Lloyd, J.W.: Foundations of Logic Programming. Springer, Berlin (1988)
Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In Minker, J., ed.: Foundations of Deductive Databases and Logic Programming. Morgan Kaufmann, Los Altos, CA (1988) 89-148
Hitzler, P., Hölldobler, S., Seda, A.K.: Logic programs and connectionist net-works. Journal of Applied Logic 3 (2004) 245-272
d’Avila Garcez, A.S., Zaverucha, G., de Carvalho, L.A.V.: Logical inference and inductive learning in artificial neural networks. In Hermann, C., Reine, F., Strohmaier, A., eds.: Knowledge Representation in Neural networks. Logos Verlag, Berlin (1997) 33-46
d’Avila Garcez, A.S., Broda, K.B., Gabbay, D.M.: Neural-Symbolic Learning Systems — Foundations and Applications. Perspectives in Neural Computing. Springer, Berlin (2002)
Kalinke, Y.: Ein massiv paralleles Berechnungsmodell für normale logische Pro-gramme. Master’s thesis, TU Dresden, Fakultät Informatik (1994) (in German).
Seda, A., Lane, M.: Some aspects of the integration of connectionist and logic-based systems. In: Proceedings of the Third International Conference on Infor-mation, International Information Institute, Tokyo, Japan (2004) 297-300
d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: A connectionist inductive learning system for modal logic programming. In: Proceedings of the IEEE International Conference on Neural Information Processing ICONIP’02, Singa-pore. (2002)
d’Avila Garcez, A.S., Lamb, L.C., Gabbay, D.M.: Neural-symbolic intuitionistic reasoning. In A. Abraham, M.K., Franke, K., eds.: Frontiers in Artificial Intel-ligence and Applications, Melbourne, Australia, IOS Press (2003) Proceedings of the Third International Conference on Hybrid Intelligent Systems (HIS’03).
Andrews, R., Diederich, J., Tickle, A.: A survey and critique of techniques for extracting rules from trained artificial neural networks. Knowledge-Based Systems 8 (1995)
Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2 (1989) 359-366
Funahashi, K.I.: On the approximate realization of continuous mappings by neural networks. Neural Networks 2 (1989) 183-192
Hölldobler, S., Kalinke, Y., Störr, H.P.: Approximating the semantics of logic programs by recurrent neural networks. Applied Intelligence 11 (1999) 45 58
Willard, S.: General Topology. Addison-Wesley (1970)
Fitting, M.: Metric methods, three examples and a theorem. Journal of Logic Programming 21 (1994) 113-127
Bader, S., Hitzler, P., Witzel, A.: Integrating first-order logic programs and con-nectionist systems - a constructive approach. In d’Avila Garcez, A.S., Elman, J., Hitzler, P., eds.: Proceedings of the IJCAI-05 Workshop on Neural-Symbolic Learning and Reasoning, NeSy’05, Edinburgh, UK. (2005)
Witzel, A.: Integrating first-order logic programs and connectionist systems - a constructive approach. Project thesis, Department of Computer Science, Technische Universität Dresden, Dresden, Germany (2005)
Barnsley, M.: Fractals Everywhere. Academic Press, San Diego, CA, USA (1993)
Witzel, A.: Neural-symbolic integration - constructive approaches. Master’s thesis, Department of Computer Science, Technische Universität Dresden, Dresden, Germany (2006)
Bader, S., Hitzler, P., Hölldobler, S., Witzel, A.: A fully connectionist model generator for covered first-order logic programs. In Veloso, M.M., ed.: Proceed-ings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI-07), Hyderabad, India, Menlo Park CA,  AAAI Press (2007) 666-671
Fritzke, B.: Vektorbasierte Neuronale Netze. Habilitation, Technische Univer-sität Dresden (1998)
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Bader, S., Hitzler, P., Hölldobler, S., Witzel, A. (2007). The Core Method: Connectionist Model Generation for First-Order Logic Programs. In: Hammer, B., Hitzler, P. (eds) Perspectives of Neural-Symbolic Integration. Studies in Computational Intelligence, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73954-8_9
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