A Dynamic Binding Mechanism for Retrieving and Unifying Complex Predicate-Logic Knowledge

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.

[1]  Gadi Pinkus.  Constructing Proofs in Symmetric Networks , 1991, NIPS.

[2]  R. Jackendoff.  Foundations of Language: Brain, Meaning, Grammar, Evolution , 2002 .

[3]  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.

[4]  Dov M. Gabbay,et al.  Neural-Symbolic Cognitive Reasoning , 2008, Cognitive Technologies.

[5]  Andreas Stolcke,et al.  Unification as Constraint Satisfaction in Structured Connectionist Networks , 1989, Neural Computation.

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

[7]  Steffen Hölldobler.  A Structured Connectionist Unification Algorithm , 1990, AAAI.

[8]  B. Fronhöfer,et al.  Parallelization in Inference Systems , 1992, Lecture Notes in Computer Science.

[9]  Tony A. Plate,et al.  Holographic reduced representations , 1995, IEEE Trans. Neural Networks.

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

[11]  Antony Browne,et al.  Connectionist variable binding , 1999, Expert Syst. J. Knowl. Eng..

[12]  G. Striedter.  Précis of Principles of Brain Evolution , 2006, Behavioral and Brain Sciences.

[13]  F. Velde,et al.  Neural blackboard architectures of combinatorial structures in cognition , 2006 .

[14]  Jerome A. Feldman,et al.  A (Somewhat) New Solution to the Variable Binding Problem , 2008, Neural Computation.

[15]  Mike Paterson,et al.  Linear unification , 1976, STOC '76.

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

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

[18]  J. Fodor,et al.  Connectionism and cognitive architecture: A critical analysis , 1988, Cognition.

[19]  Pascal Hitzler,et al.  Connectionist model generation: A first-order approach , 2008, Neurocomputing.

[20]  Ulrich Berger,et al.  Computational Logic , 2001, NATO ASI Series.

[21]  Ekaterina Komendantskaya,et al.  Unification neural networks: unification by error-correction learning , 2011, Log. J. IGPL.