Parallel Logical Inference and Energy Minimization

The inference capabilities of humans suggest that they might be using algorithms with high degrees of parallelism. This paper develops a completely parallel connectionist inference mechanism. The mechanism handles obvious inferences, where each clause is only used once, but may be extendable to harder cases. The main contribution of this paper is to show formally that some inference can be reduced to an energy minimization problem in a way that is potentially useful.

[1]  Sharon Sickel,et al.  A Search Technique for Clause Interconnectivity Graphs , 1976, IEEE Transactions on Computers.

[2]  Lawrence J. Henschen Introduction: Tutorial on Resolution , 1976, IEEE Trans. Computers.

[3]  Geoffrey E. Hinton,et al.  OPTIMAL PERCEPTUAL INFERENCE , 1983 .

[4]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[5]  Martin D. Davis,et al.  Obvious Logical Inferences , 1981, IJCAI.

[6]  Jerome A. Feldman Energy and the Behavior of Connectionist Models. , 1985 .

[7]  J. A. Robinson,et al.  A Machine-Oriented Logic Based on the Resolution Principle , 1965, JACM.

[8]  J J Hopfield,et al.  Neural networks and physical systems with emergent collective computational abilities. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[9]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[11]  Nils J. Nilsson,et al.  Principles of Artificial Intelligence , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  W. W. Bledsoe,et al.  Review of "Problem-Solving Methods in Artificial Intelligence by Nils J. Nilsson", McGraw-Hill Pub. , 1971, SGAR.

[13]  Jerome A. Feldman,et al.  Connectionist Models and Their Properties , 1982, Cogn. Sci..

[14]  Robert A. Kowalski,et al.  A Proof Procedure Using Connection Graphs , 1975, JACM.

[15]  Eugene C. Freuder Synthesizing constraint expressions , 1978, CACM.

[16]  Nils J. Nilsson,et al.  Problem-solving methods in artificial intelligence , 1971, McGraw-Hill computer science series.

[17]  David S. Touretzky,et al.  Cancellation in a Parallel Semantic Network , 1981, IJCAI.