Applying connectionist modal logics to distributed knowledge representation problems

Neural-Symbolic Systems concern the integration of the symbolic and connectionist paradigms of Artificial Intelligence. Distributed knowledge representation is traditionally seen under a symbolic perspective. In this paper, we show how neural networks can represent distributed symbolic knowledge, acting as multi-agent systems with learning capability (a key feature of neural networks). We apply the framework of Connectionist Modal Logics to well-known testbeds for distributed knowledge representation formalisms, namely the muddy children and the wise men puzzles. Finally, we sketch a full solution to these problems by extending our approach to deal with knowledge evolution over time.

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

[2]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[3]  Dov M. Gabbay,et al.  The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems , 1987, Temporal Logic in Specification.

[4]  Geoffrey E. Hinton,et al.  Learning internal representations by error propagation , 1986 .

[5]  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..

[6]  Frédéric Alexandre,et al.  Connectionist-Symbolic Integration: From Unified to Hybrid Approaches , 1996 .

[7]  Michael Zakharyaschev,et al.  Modal Logic , 1997, Oxford logic guides.

[8]  A.S. d'Avila Garcez,et al.  Extended theory refinement in knowledge-based neural networks , 2002, Proceedings of the 2002 International Joint Conference on Neural Networks. IJCNN'02 (Cat. No.02CH37290).

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

[10]  Ron Sun,et al.  Robust Reasoning: Integrating Rule-Based and Similarity-Based Reasoning , 1995, Artif. Intell..

[11]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[12]  Thomas Eiter,et al.  Preferred Answer Sets for Extended Logic Programs , 1999, Artif. Intell..

[13]  Yasubumi Sakakibara Programming in Modal Logic: An Extension of PROLOG based on Modal Logic , 1986, LP.

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

[15]  Artur S. d'Avila Garcez,et al.  Reasoning about Time and Knowledge in Neural Symbolic Learning Systems , 2003, NIPS.

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

[17]  M. Fitting Proof Methods for Modal and Intuitionistic Logics , 1983 .

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

[19]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

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

[21]  Gadi Pinkas,et al.  Reasoning, Nonmonotonicity and Learning in Connectionist Networks that Capture Propositional Knowledge , 1995, Artif. Intell..

[22]  Lokendra Shastri,et al.  Advances in SHRUTI—A Neurally Motivated Model of Relational Knowledge Representation and Rapid Inference Using Temporal Synchrony , 1999, Applied Intelligence.

[23]  Wanli Ma,et al.  An Overview of Temporal and Modal Logic Programming , 1994, ICTL.

[24]  Artur S. d'Avila Garcez,et al.  The Connectionist Inductive Learning and Logic Programming System , 1999, Applied Intelligence.

[25]  Krysia Broda,et al.  Symbolic knowledge extraction from trained neural networks: A sound approach , 2001, Artif. Intell..

[26]  Jude W. Shavlik,et al.  Knowledge-Based Artificial Neural Networks , 1994, Artif. Intell..

[27]  Vipin Kumar,et al.  Rule-based reasoning in connectionist networks , 1997 .

[28]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[29]  Steffen Hölldobler,et al.  Automated Inferencing and Connectionist Models , 1993 .

[30]  Dov M. Gabbay,et al.  Labelled Deductive Systems: Volume 1 , 1996 .

[31]  Alessandra Russo,et al.  Generalising Propositional Modal Logic Using Labelled Deductive Systems , 1996, FroCoS.