Kai-Yeung Siu Dept. of Electrical & Computer Engineering University of California, Irvine Irvine, CA 92717 Jehoshua Bruck IBM Research Division Almaden Research Center San Jose, CA 95120-6099 Abstract An important issue in neural computation is the dynamic range of weights in the neural networks. Many experimental results on learning indicate that the weights in the networks can grow prohibitively large with the size of the inputs. Here we address this issue by studying the tradeoffs between the depth and the size of weights in polynomial-size networks of linear threshold elements (LTEs). We show that there is an efficient way of simulating a network of LTEs with large weights by a network of LTEs with small weights. To prove these results, we use tools from harmonic analysis of Boolean functions.

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.

There is substantial evidence that AI technology can meet the requirements of the large potential market that will exist for knowledge-based software engineering at the turn of the century. In this article, which forms the conclusion to the AAAI Press book Automating Software Design, edited by Michael Lowry and Robert McCartney, Michael Lowry discusses the future of software engineering, and how knowledge-based software engineering (KBSE) progress will lead to system development environments. Specifically, Lowry examines how KBSE techniques promote additive programming methods and how they can be developed and introduced in an evolutionary way.

In COLT-92, pp. 128–135.

A Prolog technology theorem prover (PTTP) is an extension of Prolog that is complete for the full first-order predicate calculus. It differs from Prolog in its use of unification with the occurs check for soundness, depth-first iterative-deepening search instead of unbounded depth-first search to make the search strategy complete, and the model elimination reduction rule that is added to Prolog inferences to make the inference system complete. This paper describes a new Prolog-based implementation of PTTP. It uses three compile-time transformations to translate formulas into Prolog clauses that directly execute, with the support of a few run-time predicates, the model elimination procedure with depth-first iterative-deepening search and unification with the occurs check. Its high performance exceeds that of Prolog-based PTTP interpreters, and it is more concise and readable than the earlier Lisp-based compiler, which makes it superior for expository purposes. Examples of inputs and outputs of the compile-time transformations provide an easy and precise way to explain how PTTP works.

"We introduce a greedy local search procedure called GSAT for solving propositional satisfiability problems. Our experiments show that this procedure can be used to solve hard, randomly generated problems that are an order of magnitude larger than those that can be handled by more traditional approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also discussed. GSAT is best viewed as a model-finding procedure. Its good performance suggests that it may be advantageous to reformulate reasoning tasks that have traditionally been viewed as theorem-proving problems as model-finding tasks." Proc. AAAI-92.

In this article, we present some results of our research focusing on the use of our newest automated reasoning program OTTER to prove theorems from Robbins algebra, equivalential calculus, implicational calculus, combinatory logic, and finite semigroups. Included among the results are answers to open questions and new shorter and less complex proofs to known theorems. To obtain these results, we relied upon our usual paradigm, which heavily emphasizes the role of demodulation, subsumption, set of support, weighting, paramodulation, hyperresolution, and UR-resolution. Our position is that all of these components are essential, even though we can shed little light on the relative importance of each, the coupling of the various components, and the metarules for making the most effective choices. Indeed, without these components, a program will too often offer inadequate control over the redundancy and irrelevancy of deduced information.

Academic Press.

A sound and complete theorem prover for first-order logic is presented, which is based on the connection method. The inference machine is implemented using PROLOG technology, an approach taken also with other systems, most prominently with Stickel's PTTP. But SETHEO differs from those in essential characteristics, among which are the following ones. It incorporates a powerful preprocessing module for a reduction of the input formula. The main proof procedure is realized as a variant of Warren's abstract machine.

Viewing n-variable boolean functions as vectors in'R'2", we invoke tools from linear algebra and linear programming to derive new results on the realizability of boolean functions using threshold gat.es. Using this approach, one can obtain: (1) upper-bounds on the number of spurious memories in HopfielJ networks, and on the number of functions implementable by a depth-d threshold circuit; (2) a lower bound on the number of ort.hogonal input.