A Fascinating Country in the World of Computing

Abstract

To me, this progress has been truly awesome. Larry Wos understands the events that led to this progress more thoroughly than anyone else I have met. He was there in 1963, working with J. A. Robinson and George Robinson at Argonne, when resolution was discovered. He has been part of many steps forward since then, and continues focusing on the issue of how to get programs to pluck proofs of theorems from huge spaces of logical formulas.Larry has played a unique role in the development of automated deduction systems. His ideas have repeatedly led to significant, and often fundamental, advances. A few of us have been fortunate enough to discuss these ideas with him frequently over the years, but most of the community is largely unfamiliar with Larry and his rather unorthodox approach to research. Certainly, his papers say a great deal and have reached a wide audience, but there is far more to what occurred than appears in those published papers. His earlier books were serious attempts to capture the essential positions and techniques (and to do so in a way that would entertain as well as educate). Yet there is much more to be said about the views, insights, and experiences that make up Larry's perspective on the field. Certainly this book is not comprehensive either; however, it does, as those before it have, uniquely capture aspects of Larry's views and the experiments that shaped them.Different classes of researchers will approach the material in this book from widely differing backgrounds, and what they wish to extract will also vary considerably. A few will approach it with the same motives I had in forming a relationship with Larry-a desire to understand how to build more powerful systems. Far more will wish to learn about how to use a program such as OTTER to attack problems in logic and mathematics. Others will simply be trying to formulate a reasonable overview of the field. In each case, I believe that there are critical lessons to be learned from both this book and the separate two-volume book of his collected papers. For me, one of those lessons is foremost: You must play with problems if you hope to get insight. People often believe that they can predict accurately what will be the outcome of an experiment in automated deduction, but my experience indicates that it is seldom the case. By providing a copy of OTTER-a wonderful tool developed by William McCune-Larry has given you the opportunity to easily encode and run problems that vary from extremely simple exercises to open questions in mathematics.I am tempted to try to summarize what I think is really important in Larry's work, but that would be foolish-you, the reader, should try to understand Larry's perspective, not my understanding of it. Instead, let me describe my first encounter with Larry's work: the paper in which he introduced paramodulation (Robinson and Wos 1969). I was a young graduate student attempting to define a thesis project. When I read the paper, I basically ignored Wos's opinions and focused on the problem he posed (a modestly di...

Finding Proofs in Tarskian Geometry

“…It is not an introduction to OTTER but an attempt to make the subsequent information about our methodology comprehensible to those who do not have expertise with OTTER; at least, it should enable such readers to make sense of the input files and proofs we exhibit on the project's website [1]. For more information about OTTER, see [25].…”

“…-Use a propitious combination of rules of inference. For an introduction to these rules please refer to [25]. -One can exert some control over which clause will be selected from sos at the next iteration by using OTTER's pick given ratio.…”

Rectangular quasigroups and rectangular loops

“…Not surprisingly then, most new mathematics to come out of automated reasoning has been in fields close to algebra. For general methods for applying automated reasoning to problems in mathematics and other areas, see the book by Wos and Pieper [10]. New results proved by OTTER in particular can be found in the book by McCune and Padmanabhan [11].…”

Reasoning about the Properties of an Enterprise Information System

“…It is furthermore an open problem as to which inference rule would build set theory into a theorem prover the same way as paramodulation builds in equality-oriented reasoning [8]. Paramodulation is a rule applied to a pair of clauses and requiring that at least one of the two contains a positive equality literal, and yielding a clause in which an equality substitution corresponding to the equality literal has occurred.…”