Abstract not found

Every mathematician will agree that the discovery, analysis, and communication

ABSTRACT. Logic can be defined as the formal study of reasoning; if we replace "for-mal " by "mechanical " we can place almost the entire set of methodologies used in the field of automated theorem proving (ATP) within the scope of logic. Because of the goals of ATP, if not always the methodologies, ATP has been considered to be within the domain of AI. We explore the methodologies of ATP, including the logics that underlie the theorem provers, and discuss some of the mechanisms that utilize these logics. These include term rewriting systems, mathematical induction, inductionless induction and even mixed integer programming. The ATP field, via resolution, has even provided the foundation for an exciting AI and database programming language, PROLOG. We conclude with a new method for extending the PROLOG system to work with non-Horn clause sets within a positive logic format, particularly simple for "slightly non-Horn " clause sets.

Abstract. This paper surveys the field of automated reasoning, giving some historical background and outlining a few of the main current research themes. We particularly emphasize the points of contact and the contrasts with computer algebra. We finish with a discussion of the main applications so far. 1 Historical introduction The idea of reducing reasoning to mechanical calculation is an old dream [75]. Hobbes [55] made explicit the analogy in the slogan ‘Reason [...] is nothing but Reckoning’. This parallel was developed by Leibniz, who envisaged a ‘characteristica universalis’ (universal language) and a ‘calculus ratiocinator ’ (calculus of reasoning). His idea was that disputes of all kinds, not merely mathematical ones, could be settled if the parties translated their dispute into the characteristica and then simply calculated. Leibniz even made some steps towards realizing this lofty goal, but his work was largely forgotten. The characteristica universalis The dream of a truly universal language in Leibniz’s sense remains unrealized and probably unrealizable. But over the last few centuries a language that is at least adequate for

An automated reasoning program has provided invaluable assistance in answering certain previously open questions in mathematics and in formal logic. These questions would not have been answered, at least by those who obtained the results, were it not for the program's contribution. Others have used such a program to design logic circuits, many of which proved superior (with respect to transistor count) to the existing designs, and to validate the design of other circuits. These successes establish the value of an automated reasoning program for research and suggest the value for practical applications. We thus conclude that the field of automated reasoning is on the verge of becoming one of the more significant branches of computer science. Further, we conclude that the field has already advanced from stage 1, that of potential usefulness, to stage 2, that of actual usefulness. To pass to stage 3, that of wide acceptance and use, requires, among other things, easy access to an automated reasoning program and an understanding of the various aspects of automated reasoning. In fact, an automated reasoning program is available that is portable and can be run on relatively inexpensive machines. Moreover, a system exists for producing a reasoning program tailored to given specifications. As for the requirement of understanding the aspects of automated reasoning, much research remains—research aided by access to a reasoning program. A large obstacle has thus been removed, permitting many to experiment with and find uses for a computer program that can be relied upon as a most valuable automated reasoning assistant.

Abstract not found