Connectionist model generation: A first-order approach

Knowledge-based artificial neural networks have been applied quite successfully to propositional knowledge representation and reasoning tasks. However, as soon as these tasks are extended to structured objects and structure-sensitive processes as expressed e.g., by means of first-order predicate logic, it is not obvious at all what neural-symbolic systems would look like such that they are truly connectionist, are able to learn, and allow for a declarative reading and logical reasoning at the same time. The core method aims at such an integration. It is a method for connectionist model generation using recurrent networks with feed-forward core. We show in this paper how the core method can be used to learn first-order logic programs in a connectionist fashion, such that the trained network is able to do reasoning over the acquired knowledge. We also report on experimental evaluations which show the feasibility of our approach.

[1]  Gadi Pinkas,et al.  Symmetric Neural Networks and Propositional Logic Satisfiability , 1991, Neural Computation.

[2]  Kai-Uwe Kühnberger,et al.  Learning Models of Predicate Logical Theories with Neural Networks Based on Topos Theory , 2007, Perspectives of Neural-Symbolic Integration.

[3]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[4]  Melvin Fitting,et al.  Metric Methods Three Examples and a Theorem , 1994, J. Log. Program..

[5]  Pascal Hitzler,et al.  Logic programs, iterated function systems, and recurrent radial basis function networks , 2004, J. Appl. Log..

[6]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[7]  Sebastian Bader,et al.  The Core Method: Connectionist Model Generation , 2006, ICANN.

[8]  Steffen Hölldobler,et al.  Approximating the Semantics of Logic Programs by Recurrent Neural Networks , 1999, Applied Intelligence.

[9]  W. Pitts,et al.  A Logical Calculus of the Ideas Immanent in Nervous Activity (1943) , 2021, Ideas That Created the Future.

[10]  A. Seda,et al.  Some Aspects of the Integration of Connectionist and Logic-Based Systems † , 2006 .

[11]  Joachim Diederich,et al.  Survey and critique of techniques for extracting rules from trained artificial neural networks , 1995, Knowl. Based Syst..

[12]  Lokendra Shastri,et al.  SHRUTI: A Neurally Motivated Architecture for Rapid, Scalable Inference , 2007, Perspectives of Neural-Symbolic Integration.

[13]  Dov M. Gabbay,et al.  Dimensions of Neural-symbolic Integration - A Structured Survey , 2005, We Will Show Them!.

[14]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[15]  P. Smolensky.  On variable binding and the representation of symbolic structures in connectionist systems , 1987 .

[16]  Krysia Broda,et al.  Neural-symbolic learning systems - foundations and applications , 2012, Perspectives in neural computing.

[17]  John McCarthy,et al.  Epistemological challenges for connectionism , 1988, Behavioral and Brain Sciences.

[18]  Dana H. Ballard,et al.  Parallel Logical Inference and Energy Minimization , 1986, AAAI.

[19]  Heekuck Oh,et al.  Neural Networks for Pattern Recognition , 1993, Adv. Comput..

[20]  Jude W. Shavlik,et al.  Extracting Refined Rules from Knowledge-Based Neural Networks , 1993, Machine Learning.

[21]  Michael G. Dyer,et al.  High-level Inferencing in a Connectionist Network , 1989 .

[22]  Steffen Hölldobler,et al.  Towards a New Massively Parallel Computational Model for Logic Programming , 1994 .

[23]  John Wylie Lloyd,et al.  Foundations of Logic Programming , 1987, Symbolic Computation.

[24]  Jack Minker.  Foundations of deductive databases and logic programming , 1988 .

[25]  Artur S. d'Avila Garcez,et al.  We Will Show Them! Essays in Honour of Dov Gabbay, Volume One , 2005, We Will Show Them!.

[26]  A. Seda.  Topology And The Semantics Of Logic Programs , 1995 .

[27]  Franz J. Kurfess,et al.  CHCL - A Connectionist Infernce System , 1990, Dagstuhl Seminar on Parallelization in Inference Systems.

[28]  Pascal Hitzler,et al.  Perspectives of Neural-Symbolic Integration , 2007, Studies in Computational Intelligence.

[29]  Franz Kurfess,et al.  Chcl -a Connectionist Inference System , 1991 .

[30]  Pascal Hitzler,et al.  Logic programs and connectionist networks , 2004, J. Appl. Log..

[31]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[32]  A.S. d'Avila Garcez,et al.  A connectionist inductive learning system for modal logic programming , 2002, Proceedings of the 9th International Conference on Neural Information Processing, 2002. ICONIP '02..

[33]  L. Shastri,et al.  From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony , 1993, Behavioral and Brain Sciences.

[34]  Andreas Witzel,et al.  A Fully Connectionist Model Generator for Covered First-Order Logic Programs , 2007, IJCAI.