This paper considers the problem of expressing predicate calculus in connectionist networks that are based on energy minimization. Given a firstorder-logic knowledge base and a bound k, a symmetric network is constructed (like a Boltzman machine or a Hopfield network) that searches for a proof for a given query. If a resolution-based proof of length no longer than k exists, then the global minima of the energy function that is associated with the network represent such proofs. The network that is generated is of size cubic in the bound k and linear in the knowledge size. There are no restrictions on the type of logic formulas that can be represented.

This paper considers the problem of expressing predicate calculus in connectionist networks that are based on energy minimization. Given a firstorder-logic knowledge base and a bound k, a symmetric network is constructed (like a Boltzman machine or a Hopfield network) that searches for a proof for a given query. If a resolution-based proof of length no longer than k exists, then the global minima of the energy function that is associated with the network represent such proofs. The network that is generated is of size cubic in the bound k and linear in the knowledge size. There are no restrictions on the type of logic formulas that can be represented.

This paper considers the problem of expressing predicate calculus in connectionist networksthat are based on energy minimization. Given a firstorder-logic knowledgebase and a bound k, a symmetric network is constructed (like a Boltzman machine or a Hopfield network) that searches for a proof for a given query. If a resolution-based proof of length no longer than k exists, then the global minima of the energy function that is associated with the network represent such proofs. The network that is generated is of size cubic in the bound k and linear in the knowledge size. There are no restrictions on the type of logic formulas that can be represented.

Industrial managers, engineers, and technologists have many expectations from artificial intelligence and its application to knowledge-based systems. Although the past decade has witnessed a number of innovative applications of AI in manufacturing, the field is still in its infancy and holds even greater promise for the future. The AAAI Press book Artificial Intelligence Applications in Manufacturing, (from which the following article was selected) presents a number of articles that relate to the enhancement of planning and decision making capabilities in today's automated production environments.

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem.

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques.

In Shapiro, S. (Ed.), Encyclopedia of Artificial Intelligence., Vol. 1, pp. 285-293. Wiley. Links to a variety of constraint satisfaction articles. The complexity of some polynomial network consistency algorithms for constraint satisfaction problems. Artificial Intelligence, Volume 25, Issue 1, January 1985, Pages 65–74 (http://www.sciencedirect.com/science/article/pii/0004370285900414). Constraint Satisfaction. Technical Report, University of British Columbia, 1985 (http://dl.acm.org/citation.cfm?id=901711). The logic of constraint satisfaction. Artificial Intelligence, Volume 58, Issues 1–3, December 1992, Pages 3–20 (http://www.sciencedirect.com/science/article/pii/000437029290003G). The complexity of constraint satisfaction revisited. Artificial Intelligence, Volume 59, Issues 1–2, February 1993, Pages 57–62 (http://www.sciencedirect.com/science/article/pii/000437029390170G). Parallel and distributed algorithms for finite constraint satisfaction problems. Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing, 1991 (https://ieeexplore.ieee.org/document/218214). Hierarchical arc consistency: exploiting structured domains in constraint satisfaction problems. Computational Intelligence, Volume 1, Issue 1, pages 118–126, January 1985 (https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-8640.1985.tb00064.x). Knowledge structuring and constraint satisfaction: the Mapsee approach. IEEE Transactions on Pattern Analysis and Machine Intelligence (Volume:10, Issue: 6) (https://ieeexplore.ieee.org/abstract/document/9108?section=abstract). Chapter 2 – Constraint Satisfaction: An Emerging Paradigm. Foundations of Artificial Intelligence, Volume 2, 2006, Pages 13–27. Handbook of Constraint Programming (http://www.sciencedirect.com/science/article/pii/S1574652606800064).

The CLP( ℛ) programming language is defined, its underlying philosophy and programming methodology are discussed, important implementation issues are explored in detail, and finally, a prototype interpreter is described. CLP( ℛ) is designed to be an instance of the Constraint Logic Programming Scheme, a family of rule-based constraint programming languages defined by Jaffar and Lassez. The domain of computation ℛ of this particular instance is the algebraic structure consisting of uninterpreted functors over real numbers. An important property of CLP( ℛ)is that the constraints are treated uniformly in the sense that they are used to specify the input parameters to a program, they are the only primitives used in the execution of a program, and they are used to describe the output of a program. Implementation of a CLP language, and of CLP( ℛ) in particular, raises new problems in the design of a constraint-solver.

AI Magazine, 13 (1), 32-44.

In AAAI- 92, pp. 622–627.