Appendix: Conjectures Concerning Proof, Design, and Verification

This article focuses on an esoteric but practical use of automated reasoning that may indeed be new to many, especially those concerned primarily with verification of both hardware and software. Specifically, featured are a discussion and some methodology for taking an existing design -- of a circuit, a chip, a program, or the like--and refining and improving it in various ways. Although the methodology is general and does not require the use of a specific program, McCune's program OTTER does offer what is needed. OTTER has played and continues to play the key role in my research, and an interested person can gain access to this program in various ways, not the least of which is through the included CD-ROM in [3]. When success occurs, the result is a new design that may require fewer components, avoid the use of certain costly components, offer more reliability and ease of verification, and, perhaps most important, be more efficient in the contexts of speed and heat generation. Although the author has minimal experience in circuit design, circuit validation, program synthesis, program verification, and similar concerns, (at the encouragement of colleagues based on successes to be cited) he presents materials that might indeed be of substantial interest to manufacturers and programmers. He writes this article in part prompted by the recent activities of chip designers that include Intel and AMD, activities heavily emphasizing the proving of theorems. As for his research that appears to the author to be relevant, he has made an intense and most profitable study of finding proofs that are shorter [2,3], some that avoid the use of various types of term, some that are far less complex than previously known, and the like. Those results suggest to me a strong possible connection between more appealing proofs (in mathematics and in logic) and enhanced and improved design of both hardware and software. Here the author explores diverse conjectures that elucidate some of the possibly fruitful connections

Benchmark problems in which equality plays the major role

We have recently heard rumors that researchers are again studying paramodulation (Wos87) in the context of strategy for its control. In part to facilitate such research, and in part to provide test problems for evaluating other approaches to equality-oriented reasoning, we offer in this article a set of benchmark problems in which equality plays the dominant role. The test problems are taken from group theory, Robbins algebra, combinatory logic, and other areas. For each problem, we include appropriate clauses and comment as to its status with regard to provability by an unaided automated reasoning program

Automatd generation of models and counterexamples and its application to open questions in Ternary Boolean algebra

The purposes of this paper are to answer certain previously unanswered questions in the field of Ternary Boolean algebra; to describe the method, by use of an automated theorem-proving program as an invaluable aid, by which these answers were obtained; and to give informally the characteristics of those problems to which the method can be successfully applied. The approach under study begins with known facts in the form of axioms and lemmas of the field being investigated, finds by means of certain specified inference rules new facts, and continues to reason from the expanding set of facts until the problem at hand is solved or the procedure is interrupted. The solution often takes the form of a finite model or of a counter-example to the underlying conjecture. The model and/or counterexample is generated with the aid of an already existing automated theorem-proving procedure and without any recourse to any additional programing

Immunodepletion in xenotransplantation

Xenograft transplantation is perhaps the most immunologically difficult problem in transplantation today. An overwhelming hyperacute rejection reaction (HAR) occurs within minutes of organ implantation. Preformed antibodies are thought to initiate this process. We used a pig-to-dog renal xenograft transplant model and investigated methods of decreasing the severity of hyperacute rejection. Female pigs weighing 15-20 kg were used as donors. Recipients were mongrel dogs weighing 15-25 kg. Experimental dogs were all given a number of treatments of IgG depletion using an antibody removal system (Dupont-Excorim). This machine immunoadsorbs plasma against a column containing immobilized staphylococcal protein A, which is known to bind the IgG Fc receptor. An 84% reduction in the IgG levels and a 71% reduction in IgM levels was achieved. Postoperative assessment was made of urine output, time to onset of HAR, and histopathological examination of the rejected kidneys. Although cross-matches between donor lymphocytes and recipient sera remained strongly positive in the treated dogs, there was a two- to fourfold reduction in the titers. The time to onset of HAR was prolonged in the experimental group, and the urine output was increased slightly. The histopathologic changes in the experimental group generally showed signs of HAR, but of less intensity than in the nonimmunodepleted control group. © 1990 Informa UK Ltd All rights reserved: reproduction in whole or part not permitted

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

Acute Leriche syndrome due to the thrombus in the left ventricle.

Abstract. In this contribution we present a variant of a resolution theorem prover which selects resolution steps based on the proportion of models a newly generated clause satisfies compared to all models given in a reference class. This reference class is generated from a subset of the initial clause set. Since the empty clause does not satisfy any models, preference is given to such clauses which satisfy few models only. Because computing the number of models is computationally expensive on the one hand, but will remain almost unchanged after the application of one single resolution step on the other hand, we adapt Kowalski’s connection graph method to store the number of models at each link.