The collected works of Larry Wos

1655 Pages·77.728 MB·English

by  Larry Wos, Gail W. Pieper.

THE COLLECTED WORKS
OF
LARRY WOS
Volume I
This page is intentionally left blank
THE COLLECTED WORKS
OF
LARRY WOS
Volume I
Exploring the Power
of Automated Reasoning
Larry Wos
Gail W. Pieper
Mathematics and Computer Science Division
Argonne National Laboratory
E-mail: wosimcs.anl.gov, [email protected]
Web: www.mcs.anl.gov/~wos, www.mcs.anl.gov/~pieper
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THE COLLECTED WORKS OF LARRY WOS -(Vol. I)
Exploring the Power of Automated Reasoning
Copyright C 2000 by World Scientific Publishing Co. Pte. Ltd.
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ISBN 981-02-4001-5 (Set)
ISBN 981-02-4996-9 (Vol. I)
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Foreword
The scientific enterprise known as "automated reasoning" seeks to construct
computer programs that can make original and important contributions to
mathematics. In four decades of practical work, the field has progressed from
solving very simple problems in mathematical logic to the occasional solution
of difficult, open mathematical questions.
The history of automated reasoning has been blessed with a singular leader,
namely, Larry Wos. His position as foremost leader has been clearly recognized:
• founding editor of the Journal of Automated Reasoning
• first president of the Association of Automated Reasoning
• first winner of the American Mathematical Society's current prize in au-
tomated reasoning (shared with Steven Winker)
• first winner of the Herbrand Award in Automated Deduction
His scientific papers, assembled here, constitute a very significant part of
Wos's enormous contributions to automated reasoning.
As all his friends will testify, Wos is an utterly ingenious fellow, a singular
character, a truly wonderful person. Perhaps in the spirit of a Zen master,
Wos has occasionally claimed that he is not a scientist at all. Although I know
no better scientist than Wos, I think reporting his claim not to be a scientist
will help those who have not had the privilege of knowing him to understand
the enormous energy and joy with which Wos does his work. His appetite for
inventing strategies to enhance Argonne's several automated reasoning programs
is voracious. Equally amazing is his stamina for examining in extensive detail
the results of running the Argonne programs on a multitude of examples. But I
suspect that the reason that Wos might be reluctant to claim the title scientist
is that he imagines that society would permit no proper scientist to experience
the passionate ecstasy that Wos does in carrying out his research.
Some of Wos's papers assembled here, especially the early ones, reflect the
tenor of the traditionally austere mathematical journal, so often dry as dust. The
field's early emphasis upon often sterile "completeness results" as the ultimate
criterion of achievement was an idol to which Wos necessarily paid tribute in
his earliest years. But as his later writings increasingly demonstrate, and as the
wonderful introductory vignettes reveal, Wos passionately wishes to invite his
reader to join in what Wos finds to be both the noblest and most rewarding of
human experiences, the development of the power to reason.
vi Foreword
"Reason more than anything else is man," said Aristotle. Like Aristotle, Wos
has found, and wishes to share with all, a maximal good, a thinking that is a
"thinking of thinking".
Robert Boyer
November 1998
Preface
A Life of Rewards: The Collected Works of Larry Wos
Among the various aspects of computing that have proved fascinating, you
may find the aspect covered in the papers in this two-volume set astound­
ing. Specifically, the papers focus on a challenge that certain researchers—I
included—accepted in the early 1960s and still accept. The challenge is that
of producing a single computer program that automates logical reasoning so
effectively that questions whose answers have eluded great minds for decades
will frequently yield their treasure. By reading or browsing among these papers,
you will see how progress occurred and what techniques were formulated to en­
able a program (such as William McCune's OTTER) to answer diverse open
questions and solve various hard problems. You will also share a researcher's
effort and excitement covering more than thirty-five years. Note that, with one
exception, the order of the papers in these two volumes essentially mirrors the
order in which the research occurred and the papers were written, and does not
follow the accidental order in which they were published. The exception is the
paper entitled "Resolution, Binary: Its Nature, History, and Impact on the Use
of Computers"; in particular, the 1992 version of that paper is included, rather
than the original 1987 version, to provide more up-to-date information about
OTTER and its successes.
Although the papers contained in the two volumes share a common author,
their style ranges from the very formal to the most friendly. You may be amused
by their violation of a principle of Paul Halmos: A writer should publish his
works under the same name, not vary from Lawrence Wos to Larry Wos and the
like. Finally, you will find (though not obviously) evidence of how my research
was influenced, guided, and inspired by the Significant Seven. You will learn in
this preface who they are.
As is true of my writing style and of the series of names under which I pub­
lished, the field that is the focus of the vast majority of these collected papers
underwent identity changes. In the beginning (in the early 1960s) the field was
known as mechanical theorem proving, then automatic theorem proving, then
automated theorem proving, and finally and correctly here in 1999 as automated
reasoning. (Automated deduction is a subfield, in my view, of automated reason­
ing, the latter name being introduced by me in 1980.) Far, far more significant
than the preceding is the progress that has occurred in less than four decades.
Both the amount and the rate of progress are reflected in the papers presented
in these two volumes.
Indeed, in the beginning we were pleased when a reasoning program suc­
ceeded in proving the simplest of theorems, such as the classroom exercise that
Preface
Vlll
asserts the provability of commutativity for groups in which the square of x
(for all x) is the identity e. Such an achievement by a graduate student would
provide no evidence of potential in the context of research. However, it did cor­
rectly presage what might and, eventually, did occur in the automation of logical
reasoning.
For the most startling example of the fulfillment of promise, you need only
glance at the marvelous success of my colleague William McCune in the area
of Robbins algebra. Specifically, for more than six decades (commencing in the
early 1930s), the question of whether every Robbins algebra is a Boolean alge­
bra remained open, not even yielding its treasure to such eminent scientists as
Alfred Tarski. McCune's success in answering the question is in no way isolated,
which can be seen by glancing at some of my later papers and by exploring a
monograph written by McCune and our colleague R. Padmanabhan.
If you are tempted to add to the successes and, therefore, wish targets,
I suggest A Fascinating Country in the World of Computing: Your Guide to
Automated Reasoning (the companion to this two-volume set), which offers many
hard problems and numerous open questions, especially in Chapter 11. A large
fraction of the problems and questions will appeal to you even if you have
little or no interest in automation. On the other hand, if you would enjoy the
companionship of a fine program (McCune's OTTER), the CD-ROM included
in the cited book will prove most useful.
Now, to fulfill the promise made in the beginning, I come to the Significant
Seven, in the order in which I met them. The superlatives you will encounter
are more than deserved; the gratitude that is expressed is genuine; the history
that is presented is accurate. What was immediately clear to me, as I met each
of the Seven, was that I was in the presence of a marvelous mind.
Of the Seven, George Robinson was the first. Although he resides no longer
on this planet, he is still the most logical man I have ever known. The smallest
taste of his fine insights is offered in Section 1.8 of A Fascinating Country in the
World of Computing. From him, I learned much, not the least of which concerns
experimentation and the identification of hidden premisses.
Second was Dan Carson, one of the finest computer programmers that has
ever existed. Were it not for a lack of money (in those early 1960s), he would have
obtained a Ph.D. His theorem-proving program (of the early and mid 1960s) was
clearly crucial to the field at the time and, without it, I am almost certain that
the field would have died. It remained by far the most powerful—until the third
member of the Seven arrived.
The person in question, Ross Overbeek, can only be described as brilliant.
His reasoning programs and his ideas (that include the weighting strategy and
the inference rule UR-resolution) have proved indispensable to the field. His
Pre/ace IX
influence, which will forever be vastly underestimated, can be found in the best
of all reasoning programs extant here in 1999, namely, OTTER.
The fourth of the Significant Seven is Robert Veroff. You will find little of
his work in the literature—what a loss! He continues to have ideas that increase
the power of reasoning programs. Such is not just my opinion; indeed, data
strongly supports the position, including the discovery of new fine proofs and
the formulation of techniques that he has freely given to colleagues. One of my
failings concerns my lack of success in getting him to publish his breakthroughs.
The fifth of the Seven is Steve Winker, who toured MIT in but two and
one half years, obtaining his B.A; years later, he easily obtained his Ph.D.
Unfortunately, he also published rather sparsely. He played a key role in the
Argonne group's attack on open questions in the late 1970s and the early 1980s.
His successes in Robbins algebra were crucial to McCune's remarkable result.
Robert Boyer is the sixth of the Seven. His work (with his colleague J Moore)
in program verification sets a standard that may never be matched. Boyer is the
one person I might have believed about the existence of a finite axiomatization
of set theory. Of course, he was right. He (along with his advisor Woody Bledsoe)
caused me to write my book The Automation of Reasoning: An Experimenter's
Notebook with OTTER Tutorial.
The seventh member of the Significant Seven is William McCune. He is
deservedly a legend in his own time. His program OTTER dominates my later
papers, my experimentation, and my ability to conduct research. Among other
items, he has contributed strategies of note. His work (with Padmanabhan) as
well as his other successes in answering open questions can be described only as
beautiful.
As for future greats, I suggest you follow the efforts of my latest colleague,
Branden Fitelson. In less than one year of collaboration with me, jointly and sep­
arately, he has dispatched a number of open questions. He shows more promise
than any researcher I have known since I met McCune. Branden is more than a
welcome member of the Argonne group, sharing our emphasis and requirement
of substantial experimentation.
X Preface
Acknowledgments
My deepest thanks to Robert Boyer for so many items. This two-volume set
would not exist but for his suggestion, encouragement, and insistence.
I thank William McCune for OTTER, for his aid in the preparation of the
figures in the papers offered in the two volumes, and for his collaboration that
began in the early 1980s. In automated reasoning, he has proved to be more
than wise.
I thank Branden Fitelson for his invaluable assistance and guidance in the
production of the included CD-ROM. I thank him also for restoring my belief
in the existence of students who are excited by science.
Finally, although I now break with tradition (in view of the fact that her
name appears on this book), I thank Gail Pieper for her enormous effort in
ensuring that the papers found in these two volumes meet the highest standards
of presentability. Without her contribution, the book would still be no more than
a possibility.
Larry Wos
E-mail: [email protected]
Web address: www.mcs.anl.gov/~wos/
March 1999