Communications of the ACM Communications of the ACM (Logic Programming) [35/2]

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LOGIC PROGl\AMMING

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00

0 ..,.,

"How I Got Started with Mathematica®" A few years ago, I was working with

haved, the matrices were nonsingular.

about symbolic math.

another engineer at Boeing on a project

But because of the limits of the significant

about the limits of significant digits in

digits we got with Fortran, we were run-

Fortran, C, or any other programming

I

language because with Mathematica I can

hadn't used it, I was willing to try sorting

maintain hundreds of significant digits

out the problem with Mathematica.

with no concerns about inaccuracies or

ning into this problem.

Although

Using Mathe111atica, we discovered

for the Air Force that required extensive symbolic manipulations.

of equations wasn't singular,

partial differential equations.

that it did have a solv-

My col­

league said, "Why don't we try Mathe-

able set.

matica? It does exactly what we want to

rewrote our code

do." But I'd never used it.

knowing every­

So we

I was impressed.

Fortran and were getting numerical We knew that was a

was able to handle the symbolic manipu­

mistake-the equations were well be-

lations we needed and more. [t solved dif-

eql = Coe.fficient[equation'm; the nonmember annual subscription Is $109. see top One Of malllng label tor subscrlpt!On expiration date coded In tour digits: the first two are year, last two, month Of expiration. Microfilm editions through 1980 can be purchased from Microfilm Dept., PubllShlng services Dlv.. waverly Press, 42B East Preston Street, aaltlmore, MD 21202. Microfilm and microfiche are alSo avallable from University Mlcrofllms Interna­ tional, 300 North Zeeb Road, Dept. PR, Ann Arbor, Ml 4B106; 18001521-o&OO. 51•11• copies are SB to members and $17 to nonmembers. Please send onters prepaid plus $4 tor shipping and handling to ACM onter Dept., P.O. Box 64145, Baltimore, MD 21264. FDr credit cant onters can 1800> 342·6626 Un Baltimore, Alaska, or Canada, call 13011521l-42611. Onter personnel on duty B:154:45 EST. After hours, please leave message and onter personnel wlll return your call.

M

EDITORIAL POINTERS

any people associate logic programming LP with Prolog, the language that was born in France in the early 1970s and gained attention in 1981 as the choice for Japan's ambitious Fifth Generation Computer Project. To others, logic programming brings to mind particular application domains, such as expert systems, natural language processing, compiler writing, VSLI circuit analysis, or relational databases. To yet another group logic programming will probably signify numerous combined endeavors in logic and com­ puter science that are producing fascinating developments in the areas of massively parallel architectures, operations research, numerical analysis, and the development of large, less error-prone, software packages. We hope this month's issue will provide you with fresh information about the LP field regardless of which group you fit. Communications's coverage begins with Guest Editor Jacques Cohen's overview of current topics in LP and his speculations on the future. JA. Robinson, author of the historical article, is credited with setting the path for many of the developments that followed the publication of his 1965 Journal of the ACM paper, "A Machine· Oriented Logic Based on the Resolution Principle." Following the Robinson article, John Grant and Jack M inker demonstrate the significant impact that logic programming has had on databases, particularly on the understanding of database semantics, on the extension of the concepts of relational databases, and on new techniques and tools for database users. Next, Koichi Furukawa describes the role of logic programming in Japan's Fifth Generation Project. As one of the leaders of that project, Furukawa is in an excellent position to present examples of the latest Japanese efforts. He stresses the application aspects of concurrent variants and extensions of logic pro­ gramming, which have been vigorously pursued by three groups: one at ICOT, Japan, and the other two at Imperial College, England, and the Weizmann Institute, Israel. The closing article by David S. Warren, one of the early American LP researchers, contrasts with the others in that it focuses on three specific research topics: the bottom-up evaluation of logic programs, abstract interpretations, and partial deduction. As a complement to the special section, Computing Practices features an article on implementing sets in Prolog by Toshinori Munakata. Because of its unique characteristics, Prolog requires special techniques for imple­ menting sets. Munakata presents a comprehensive overview of both existing and new methods for defining and manipulating sets in the language. Rounding out the issue is an article by Marcia C. Linn and Michael J. Clancy that examines how programmers organize their knowledge and how program design skills are commonly taught. At the core of their article is an empirical investigation that demonstrates the effectiveness of case studies for communicating the complex, multidimensional decisions necessary when designing an effective computer program. Next Month: Special Issue on CASE

WBPA

COMMUNICATIONS OF THE ACM/March 1992/Vol.35, No.3

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Executive Editor

5

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$ SIGSMALL/PC (Small & Personal Computing Systems & A p plications . . . . . .. . . . . . . . . . . . . . . . . . . . . . . 031 . . . . . . 1 7.00 . . . . . . 1 0 . 00 . . . . . . 38.00 . . + . . . 8 . 00 . . . . . 1 7 . 00 $ SIGSOFT (Software Engmeenng) . . . . . . . . . . . . . . . . . 034 . . . . . . 20.00 . . . . . . 1 0 . 00 . . . . . . 40.00 . . + . 1 3 . 00 . . . . .44.00 - $ SIGUCCS (University & College Computing Services) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 028 . . . . . . 1 5 . 00 . . . . . . . . 5.00 . . . . . . 40.00 .. + . . Free . . . . . . Free = $

'.'.'.

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.

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'.'.'.

SIG SUBTOTAL

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� .. BUSH PUSH . . .

The White House solicited input from several sci­ entific agencies and consortia when drafting the first National Tech­ nology Initiative-the Administration's latest � effort to reroute the descending curve of U.S. com­ petitiveness. Among the topics under discussion were coop­ erative R&!D partnerships, industry needs, intellectual property laws and collabora­ tive ideas. Reportedly, one of the top priorities of the Bush cabinet is to reorganize the nation's 726 laboratories to fortify the best return on federal funding. TATTLERS HOTLINE .

.

•

·�

u

.

The first Congressional computer bulletin board for whistleblowers has been announced by Rep. Bob Wise (D-WV) who will act as system operator. The Whistleblower Bulletin Board will provide an alternative means for federal employees and citi­ zens with information on government waste, fraud and abuse to contact congres­ sional investigators. The board allows two-way com­ munications between inves­ tigative staffers and potential sources; no one will be re­ quired to use his or her real name. Anyone with a PC and modem can contact the board round-the-clock all year long. Computerized files

COMMUNICATIONS OF THE ACM/March 1992/Vol.35, No.3

j

m

accepted. (202) 225-5527 . LESS THAN SUPEB . . . Britain seems to be paying the price for letting super­ computing investments lag so far behind the U.S. , Japan, Germany and Canada. Today, the average Mexican aca­ demic has greater access to supercomputers than a British counterpart, accord­ ing to a new report from the Parliamentary Office of Science and Technology. Nature magazine reports the three British academic supercomputing canters are already at capacity. Upcom­ ing environmental projects threaten to overwhelm U.K. systems. One of the penalties of the situation is that an increasing number of British academics are turning to U.S. supercomputing canters where they must make the results of their work avail­ able to all U.S. researchers. POETIC JUSTICE . . As if tax season pressures weren't .

enough, the In­ ternal Revenue Service is also dodging Congres­ sional arrows over the $8 billion, 10year Tax System Modernization (TSM). Congress has been quite critical of the way the IRS has managed and awarded contracts for TSM-an auto­ mation project racked by delays and arguments. A recent House report states "the persistence of signifi­ cant management problems in vital areas (of this proj­ ect) is a warning sign that cannot be ignored." TOO MUCH OF A GOOD THING .

. Another U.S. agency catching heat over poor management of a multi­ million dollar computer project is the National Insti­ tutes of Health. Officials at the NIH have been charged with gross overspending for equipment that was not nec­ essary or even desired. The General Accounting Office reports the NIH installed an elaborate IBM mainframe­ based computer system worth over $800 million over the last few years. NIH scientists were reportedly never consulted regarding their computer needs. If they had been, the GAO claims the majority of scientists would have been happy with a PC and have no need for the excessive automation effort. .

9

BY LAND AND SEA .

. .A $3,000 voice-activated car navigation system from Sanyo is helping Japanese drivers get where they're going. The driver com­ mands the system to zoom in and out of a map displayed on a 4-inch color screen sit­ ting on a stalk next to the driver's seat. The satellite navigation system, which the driver must program before each trip, consists of a series of map overlays stored on a CD-ROM installed in the trunk of the car. Sanyo says the system will be available in the U. S. by year-end. The race for faster sailing performance has also been enhanced by computeriza­ tion for the past few years. Digital Equipment Corp.'s America's Cup software pro­ gram has been computing data on sail shape, sail trim, rig stress, wind and overall boat performance during the race. A Digital spokes­ person told the New York Times that he foresees a day in the near future when competitors will be able to design a boat on a com­ puter, optimize it on com­ puter, build the boat and win the race. EC BIDDING .

. A newly adopted directive from the European Community will allow firms to bid across EC borders on telecommunica­ tions service contracts as of January 1, 1993. The ruling will affect all service tenders worth more than $260,000. Legislation will require the public author­ ities tendering service con­ tracts to follow open and non-

10

.

discriminatory procedures. STATUS REPORT . . . For­ eign-owned and foreign­ affiliated manufacturing plants in the U.S. use advanced manufacturing technologies such as CAD/CAM and invest more heavily in new equipment than domestic plants do. New research findings from the Rensselaer School of Management also found that new machinery and equipment investment per employee is higher in . foreign-owned and -affiliated plants. Indeed, U. S. manufacturing managers are less likely to adopt advanced technologies or to match the investment pat­ terns of domestic com­ petitors that have foreign connections. FBI JOINS CONSORTIUlVI . . .

The Federal Bureau of Investigation has joined The Microelectronics and Com­ puter Technology Corpora­ tion (MCC) as an associate member. An MCC spokes­ person explained that advanced microelectronics and computer designs are expected to play a signifi­ cant role in the technical support required by FBI HQ and field offices throughout the decade.

OLD NEWS . . . The com­ puter industry didn't fare any better than most businesses in 1991. In fact, worldwide sales revenues dropped for the first time in eight years. According to the Dataquest Inc.'s annual review, computer industry revenues dropped over 7% last year from 1990's $ll9 billion to $109. 7 billion. The only growth segment was the workstation industry which enjoyed an $8.8 billion year-an 18% increase. IBM is still the biggest PC maker, but its share shrunk by over 14% . Meanwhile, Apple's price slashing strategy paid off with a 10 .7% jump in its marketshare.

DIGESTIVE TRACKS .

. . It seems technology is easier to swallow when you have a real taste for it. Take the beaver, for instance . Just last month a hungry one dined on a Virginia-based fiber optic cable and sent a Washington, D.C. phone system to a grinding halt. Weeks earlier, USA Today reported a Kansas City air traffic control center was paralyzed for four hours when a beaver gnawed through a communications cable. These toothy critters join a growing legion of technological taste-testers which include the rat, whose antics shut down the com­ puter system at the National Association of Securities Dealers, and the sharkfest that forced AT&T to come up with an underwater repellant for its trans­ atlantic cable. 13

Ma M ; but this can b e fixed efficiently as follows: = M - ij; while j � L do begin S[Jl : = O; s(j + ijl : = O; j end if j � M then S[Jl : = O;

L Paul Pritchard

Department of Computer Science St. Lucia Queensland 4067 Australia

:=j

Let us further double the speed of Luo's sieve algorithm. The most time consuming part of the algorithm is:

Richard E. James III

3705 Eastwood Circle Santa Clara, CA 95054 �

while j � M do begin S(j] : = O; j : = + ij; ij : = t - ij; end

References l. Pritchard, P. A sublinear additive sieve for finding prime numbers. Commun. ACM 24, 3 (Jan. 198 1 ), 1 823. 2 . Pritchard, P. Fast compact prime­ number sieves (among others). j. Algorithms 4 , 4 (Dec. 1 983), 332-344.

The following replacement goes about twice as fast because it clears two elements of S in each step, still with only three statements inside the loop:

Technical Correspondence on Xuedong Luo's article first appeared in the Nov. 1 989 Communications, p. 1 367.

while j � M do begin

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XT/AT or 100% compatible with 512KB memory. 1 lloppy arive (360KBJ:

+ t;

Furthermore, note that t = 2 S [i] and this is probably easier to com­ pute than 2k + 6i.

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0 M P U T

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E R S P E C T

V E S

Charles Babbage-­ The Great uncle of computing?

On December 26, 1791, just over 200 years ago, Charles Babbage was born, the son of a rising banker, at his father's home not far from London's famous inn, the Elephant and Castle. Three months earlier Michael Faraday, son of a black­ smith, had been born a few hundred yards away. While Faraday's research work on electromagnetism and other subjects singled him out in his own lifetime as one of the most original and produc­ tive experimental physicists of the nineteeth Century, Charles Babbage was not in the same class. His present fame as an ancestral figure in the history of cornputers is a result of the spectacular success of the digital computer in our own day. This fame, however, is well deserved. Although his practical achievements were limited, he was the first to clearly see what m ight be achieved by the mechanization of computational processes . Babbage had no immediate suc­ cessor and it was not until the com­ pletion of the first working digital computers in the middle of the pres­ ent century that people began to take a renewed interest in his ideas. That there is no direct line of development from Babbage to the present day has led Doran Swade, curator of the Computing and Control collections at the Science Museum in London, to suggest that Babbage should not be regarded as the father or grand­ father of computing-he is more like a great uncle.

COMMUNICATIONS OF THE ACM/March 1992/Vol.35, No.3

The Difference Engine

B abbage ' s first idea was not a very good one, though he would never adm it it. I t was for a machine he called his "Difference Engine," and which he claimed would enable mathe­ matical tables to be computed mechanically by steam, as he once put it. The only thing a difference engine can actually do, however, is to compute and tabulate polynomials. It is true that any mathematical func­ tion can be represented piece-wise by a series of polynomials, but Babbage would have had to do a great deal of paper-and-pencil computation in order to calculate the coefficients to be set on the engine. Therefore, it was more than a lit­ tle misleading to say that a difference engine could compute mathematical tables. Babbage's defense would have been that he was concerned not so much with reducing human labor as with eliminating human mistakes, and that the Difference Engine would mechanize just those parts of the work in which human errors were particularly likely to occur. Babbage presented his proposals to the British Government in 1823 and it agreed to finance the construe-

Maurice V. Wilkes

tion of the Difference Engine. As accustomed as we are to the idea of governments providing financial support to scientists and inventors, it is easy to overlook that such a grant was almost unprecedented at that time. All went well until 1832 when Babbage had a disagreement with his engineer and work stopped. Things drifted on until 1842 when the government had to decide whether to continue or terminate the project. By then some $80,000 - a significant sum in currency of the time-had been expended and it appeared likely that as much a gain would be required. The government cannot be accused of taking the matter lightly. On the contrary, it made wide con­ sultations both directly and through the Royal Society. An important role was played by G.B. Airy, Astronomer Royal and head of the Royal Obser­ vatory at Greenwich. This was the only true scientific establishment possessed by the British government at the time, and Airy was quite used to acting as scientific adviser to the

15

CP

Mau rice v. Wilkes Cleftl and Allan Brom­ ley, a noted student of Babbage's work. paid a visit to Babbage's grave in London's Kensal Green cemetery on December 26, 1 99 1 . The date marked the 200th anniversary of Babbage's birth.

government in a variety of roles that had little to do with astronomy. Airy was hard-working and his judgment was sound. He may be regarded as the prototype of the senior government scientist of today. After going into the matter very thoroughly and making his own enquiries, Airy advised the government against sinking further money into the Difference Engine and his advice was taken. Babbage was infuriated by the decision, and from that time on had a pronounced chip on his shoulder against the British government and all its works. This is evident in his writings, particularly in his autobi­ ography published toward the end of his life. Many modern writers have taken what Babbage said at face value and charged the British government of the day with crimi­ nal shortsightedness. One frequently heard charge can

16

be disposed o f with confidence. In declining to put more money into Babbage's Difference Engine, the government did not delay the de­ velopment of the digital. computer. The Difference Engine was a spe­ cial-purpose device for aiding in the computation of mathematical tables, and was in no sense the an­ cestor of the modern digital com­ puter. Personally, I do not see how the decision eventually made by the British government can be faulted. It was not true that the Difference Engine was going to revolutionize the making of mathematical tables. This was shown clearly enough some I 0 years later when Georg and Edvard Scheutz, two Swedish engineers, built a successful differ­ ence engine. Their information was obtained from an article describing Babbage's ideas that had been pub­ lished in a technical magazine some years earlier. The Scheutz engine did what it was supposed to and was purchased for the Dudley Observa­ tory in Albany, N.Y. A copy was made for the Registrar General's office in London, an office which corresponds to the U.S. Census

Bureau. The Registrar General's office published a life table printed in part from plates prepared from stereo molds produced by the Dif­ ference Engine. However, in spite of the personal interest of William Farr who was responsible for the life table, the engine soon dropped out of use. The engine at the Dud­ ley Observatory was used to com­ pute a refraction table, but it too faded from use. The exact reasons are not re­ corded in either case. No doubt, one explanation was that the en­ gines were not very reliable. They were, I suspect, apt to make occa­ sional random mistakes. Since Bab­ bage had stressed so strongly the supposed inability of machines to make mistakes, this was a serious matter. However, it cannot be the whole story. If the engines were imperfect, steps could have been taken to improve them. The truth must be that the Scheutz engines were not seen as heralding a major revolution in the making of tables. The Analytlcal Engine

If Babbage had stopped at his Dif­ ference Engine, little more would have been heard of him. Instead, he moved on to the "Analytical Engine" which, had it been built, would have been a true general­ purpose computer (not a stored program computer in the modern sense, but more like the Harvard Mark I). Here Babbage showed vi­ sion and insight verging on genius. A good deal was published in Babbage's lifetime about this vision and about what the Analytical En­ gine might do and how it might be used. Information about the me­ chanical contrivances that Babbage conceived for its implementation remained hidden in his manuscript notebooks. When I examined these in detail in preparation for a lecture to be delivered on the centennial of his death in 1 870, I was taken aback by the richness of what I found. He discusses the design of adding mechanisms with fast-carry propa-

Macch 1992/Vol.35, No.3/COMMUNICATIONS OF THE ACM

HP asks the key software development question:

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The HP answer. C++ SoftBench. Sometimes, in the world of object­ orientecl development, the distractions can be overwhelming. But leave it to Hewlett-Packard to find an easier way to manage the complex, time-consuming tasks that so often slow you clown. C + + SoftBench is an open, integrated development environment. It allows you to stay focused on your project by reducing the number of details that demand your attention. Included in C + + SoftBench is a leading edge toolset with everything from a static analyzer to a debugger especially suited for object-oriented development. There are even tools for graphical browsing and editing of class libraries, as well as automatic source code template generation. But even the most extensive toolset isn't always enough. So C++ SoftBench gives you the ability to expand your working environment. New tools can easily be incorporated, allowing you to customize C + + SoftBench for your specific processes. The C + + SoftBe n c h Motif user interface maintains a consistent look and feel across all tools. You have the ability to program in C as well as C + +. And, of course, C + + SoftBench runs on the top UNIX® platforms, including HP and Sun. That's why C + + SoftBench is a key element of the HP CASEclge Program. To see why it should be a part of

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CP gation, scales of notation, control systems, and much more. I f Bab­ bage had published this material, it would have been of great interest in the period before electronic devices displaced mechanical ones. Babbage started working on the mechanical design of the Analytical Engine in 1 834 and continued, with some intermission, for the rest of his life. Even in his later years he was making progress in the direc­ tions of greater simplicity and greater efficiency. He began a se­ ries of successful experiments with an early form of die casting. One can understand that he was disin­ clined to publish while he felt he was still making progress. lt is sur­ prising, however, that he did not publish an early sketch written in 1 837 which bears all the signs of being intended for publication. It was written before Babbage had become immersed in detail and gives a very clear outline of what the Analytical Engine would have been like. Babbage proposed to control his machine by means of punched cards strung together as in an auto­ matic loom and behaving very much like punched paper tape. However, anyone who expects to find that Babbage anticipated mod­ ern ideas in detail will be disap­ pointed. For example, he had independently stepped card mech­ anisms to control the passage of variables to and from the store and to control the mill, as he called his arithmetical unit. He never arrived at the idea, so obvious to us, of asso­ ciating an operation code perma­ nently with the name of a variable on the same card. Nevertheless, he had the concept of loops in the pro­ gram, and he recognized that a set of cards for his engine would con­ stitute a representation of an algo­ rithm. For lower-level control, Babbage devised a system very similar to modern microprogramming with rotating barrels carrying projecting studs taking the place of the read­ only memory. The studs controlled

the action of the various parts of the machine and could also cause the barrel to step forward or back­ ward by any desired amount. Bab­ bage prepared notations for the exe­ cution of a variety of algorithms and many of these still exist. Their resemblance to modern micropro­ grams is very close and shows that Babbage thoroughly understood what we would call the art of micro­ programming. By contrast, Babbage is far from clear about how programs would be written at the user level. It is possi­ ble that he did not make any clear distinction in his mind between user-level programming and mi­ croprogramming. However, one would have expected to find some indication as to what operations would be available to the program­ mer at user level. In other words, one would have expected there to be some reference to an instruction set and some evidence that he had considered how it should be com­ posed. Nowhere in the writings that I have seen does he even touch on the matter. For me, this remains a puzzling feature of his work. Not surprisingly, Babbage had some difficulty in communicating to his contemporaries the full breadth of his vision. Toward the end of his life, he wrote that if any man "unwarned by my example" should ever succeed in building an analytical engine, "I have no fear of leaving my reputation in his charge, for he alone will be fully able to appreciate the nature of my efforts and the value of their results." Truer words than these have never been written. It was only when the first digital computers had come into action that the extent of Bab­ bage's genius became fully appreci­ ated.

COMMUNICATIONS OF THE ACM/March 1992/Vol.35, No.3

Babbage's Private Life and Personality

Babbage's intense emotional in­ volvement with the Difference En­ gine started early. In February 1 829 William Whewell-who was two years junior to Babbage and

was himself destined to achieve dis­ tinction-writes in a letter to a friend that Babbage's "anxiety about the success and fame of his machine is quite devouring and unhappy." He never admitted that the idea was not as good as he thought it was, and his feeling of resentment against the scientific establishment of the day amounted at times almost to a persecution mania. This feeling did not, how­ ever, flow over into his social life which was a great success. One senses a certain awkwardness in his dealings with people, but he must also have been a man of great charm. He knew everyone and went everywhere. Carriages crowded the street outside his house when his Saturday evening parties were in progress. Full and successful as his social life was, Babbage was lonely in his private life. After 1 3 years of very happy married life, he had the mis­ fortune to lose his wife and two of his children within a short time of each other, having lost his father not long before. It took him a long time to recover from this blow. Of his eight children, only three sons survived into adult life. A daughter of whom he was very fond died at the age of I 7. All three sons fol­ lowed careers overseas. His eldest son, Herschel, went to work on the Continent with Brunel and then migrated permanently to South Australia, where he became an important figure in the colony. The youngest son went into the military service of the East India Company. The middle son, Dugald, was not as successful in life as his brothers. He also went to South Australia. He was somewhat disapproved of by his brother Herschel for mixing with his social inferiors and being too fond, so Herschel said, of a glass of wine. I find my heart warming toward Dugald. To me he seems the most human member of that family of earnest Victorians. a Maurice V. Wilkes . received the ACM Tu.ring Award in 1 967 and is the author of Memoirs of a Computer Pioneer, MIT Press, 1 985.

21

II F

THE ASSOCIATION FOR COMJl'.��� .t:l. � . �� �HIN ERY PROUDLY PRESENTS

TH E C O M PUTER M U SEU M 'S 1 992 C O M PUTER BOWL

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CHARLIE "JOHANN SEBASTIAN"

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C H M A N vs SHOC

Captain, Asset Mana111m1nt Campany

captain, Bachman Information Systems, Inc.

B I L L "THE ELBOW"

JEFF "THE KILLER"

MACH RO N E

KA LB

MasPar Computer Corporation

ZIU·Oavls Publishing Company

D R . DAVI D L.

RUTHANN

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Alex. Brown & Sons

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ANDY "M.C. "

RAPPAPORT

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Microsoft Corporation

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vs

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D R . JOHN E. "KNOCK KNOCK"

VERN "THE ACE"

RAB U RN

Slate Corporation

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WARN O C K

Adobe Systems, Incorporated

XEROX PALO ALTO RESEARCH CENTER, CALIFORNIA

This is the rematch fans have been waiti ng for all year. Ever since the last action-packed Technical Knockout, the West has been clamoring for another go at the Champions from the East. On May 1 , they'll get their chance to lace 'em up. Join us at live at ringside or at the closed circuit site for all the blow by blow excitement of The Hassle In The Castle The Computer Museum's 4th Annual Computer Bowl. It's sure to be Another Technical Knockout.

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Presenter

The Association for Computing Machinery

Underwriters

Apple Computer, I nc. Digital Equipment Corporation

Judges

I ntel Corporation

Robertson, Stephens & Co.

The lnternetworking Company

The Computer Bowl is b road cast on the PBS series, Computer Chron icles, hosted by Stewart Che ifet. The C o m p uter Bowl is a project to benefit the educational programs of The Computer Museum, 300 Congress St., Boston, MA 0221 0 . For tickets and spons o r s h i p i n fo rmat i o n 61 7- 426-2800 ext. 346.

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A C M -TH E FI R S T S O C I ETY I N C O M P U T I N G-I S P R O U D T C S P O N S O R

The Machine That [hanged The World a

n Monday eveninCJ. April 6.

1992 at 9:00 p.m. E.S.T.. and on successive Mondays until May 4.

PBS will present The Machine Thal

[hanged the World, 5 pro[jrams on

the history of the electronic computer and its impact on society.

P

roduced by WBGH Boston

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with major funding provided by ACM and Unisys. the series hiCJhliCJhts the

fifty year revolution in computin(j and information technoloCJY-a revolution

E N I A C PHOTOGRAPH C O U RTESY THE COMPUTER M U S E U M

that is still going on.

B

Check your local PBS listings for broadcast times on the following Monday evenings: eCJinninCj with World War II

• April

research and the ENIAC. which was

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co-invented by J. Presper Eckert and • April 13-"Jnventing the Future" examines how the computer rose from

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ACM]. The Machine Thal

• April 20-"The Paperback [ompuler" explores how computers became

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unpredictable course of information technoloCJY from the room sized. data­

• April 27-"The Thinking Machine" focuses on the most ambitious goal of

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society in profound and totally unexpected ways.

A DVA N C • N G

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Dynabook Revisited­ Portable computers Past, Present and Future �,���'.:?£;?"

Much of the foundation of modern personal computing was laid over 20 years ago, when Alan Kay and his colleagues at the Xerox Palo Alto Research Center designed the Dyna­ book, a prototype portable personal computer (see Figure 1). The name "Dynabook" suggested that it would be portable (like a book), and that it was a new, dynamic medium with aspects of paper and pencil, paint, typewriter, musical instrument, and computer simulation. The first commercially impor­ tant1 portables, the Osborne 1 and the Radio Shack Model 100, had dif­ ferent goals as shown in Figure 2 . The Osborne was a portable approxi­ mation of the desktop cornputer of its day. It had the same C PU, bus, and operating system, and ran the same software as its desktop counterpart. The Model 100 was a complemen­ tary computer-an input device used in conj unction with a desktop ma­ chine. It had a text editor in ROM , and was widely used by journalists who took notes and drafted articles that were finished on a desktop computer. Today's Portables: Desktop and complementary

get by with the Zeos p o rt able , which has 5MB of memory and a 60MB disk? I ran a few benchmarks corn p a r m g t h e Zeos to AST and Goldstar desktop machines with the same CPU (16 M Hz 386SX) and memory size. As shown in Table 1, the speeds are com­ parable, with the portable losing some ground in display speed. Based on speed alone, the portable could replace many desktop computers. The major drawbacks to the port­ able are its input and output devices. The keyboard is somewhat smaller than standard, slowing down typing. This is compounded by the lack of dedicated scrolling, and asterisk keys found on the desktop machines. The portable display is also slower, lacks color, and is more difficult to read, especially when it changes rapidly (for example when moving a mouse). The portable also has no expansion slots, but with a modem and serial and parallel ports, it would satisfy many needs. If these drawbacks dissuade you, a compromise is possible. You could buy a portable computer, plus a stan-

Kay's first goal, portability in a form factor similar to the original mockup, has been achieved. Could a portable

COMMUNICATIONS OF THE ACM/ March 1992/Vol . 3 5 , No.3

Larry Press

1. Original ovnabook Mockup. While Kays goal was a machine this size, the first version of the oynabook, the "interim" oynabook, was built using a desk-sized workstation. In 1975, Kay felt hardware for a porta b l e oynabook would b e "inevitably avail· able in ten years time" !5l. That predic­ tion remains valid today.

dard keyboard and color monitor. When at your desk, the portable would be closed and plugged into the monitor and desktop keyboard. (Note that the Zeos is faster with an external display than with its LCD.) This combination would cost more than the equivalent desktop com­ puter, but not as much as a desktop computer plus a portable. If your needs demand a portable, and your budget is limited, consider this hybrid option. The Zeos portable can run Win­ dows, and generally substitute for a low-end desktop computer, but what about complementary computers, the descendants of the Model 100? ' There were earlier portables like the I B M 50xx and t h e Sony Typecorder, b u t the Osborne 1 and Model 100 were mass-marketed commercial successes.

25

PC There are two interesting options­ On the other hand, the TI display is hand-held computers and previous 5- 1 0% faster, and the machine out­ generation portables. performs many LAN servers of the There are several hand-held mid- l 980s. At 4.4 pounds, and 8 1/2 computers that run standard DOS x 1 1 x 1 .4 inches, it is easy to carry, applications. The first on the mar­ but its battery life is much less than ket was the Poqet computer. The the Poqet, which runs 1 00 hours on Poqet is 1 x 8% x 4 1/. inches and two AA batteries. The Travelmate is easier to use weighs only 1 .2 pounds. It runs for days on AA batteries. It has 5 1 2 KB than the Poqet. The keyboard is as of RAM, and DOS, BASIC, editing, easy to use as the Zeos, and the dis­ calendar, name and address, calcu­ play as easy to read. The Travel­ lator and terminal emulation soft­ mate is fine for character-based ware in ROM. Instead of disks, the applications such as word proces­ Poqet has two slots for ROM or sors, compilers, spreadsheets, and RAM cards, and ROM-card ver­ terminal emulators, but .you will sions of 1 23 and other programs have to leave your graphic user in­ are available. There is also a serial terface at home on the desk. Per­ port and a bus-extension port for haps the best thing about the adding an optional disk drive. The Travelmate is its current price­ keyboard has a standard typewriter under $800. Unless you need the layout, and by the standards of convenience of a hand-held com­ hand-held computers, it is large. puter, obsolete portables are a bar­ The display has 25 lines of 80 char­ gain. acters and 640 x 200 resolution in Tomorrow's system: graphic (CGA) mode. Since it is a standard PC, you can Dynabook plus Dynabase load your favorite software into a Alan Kay's dynamic medium was Poqet RAM card, and leave your intended for children, but I am less office. I took a Poqet to several lec­ ambitious. I would settle for a port­ tures, and discovered that it is pos­ able that helped me with profes­ sible to touch type on the keyboard, sional communication as well as but typing is slow and error-prone. with the researching, planning and 2 To make matters worse, the display writing of CACM columns . Since desktop computers will is not backlit, and I frequently found myself holding it near my always offer more performance face or maneuvering it to find suit­ .and higher bandwidth connectivity able light. I did not think the ergo­ than portables of the same price, I nomic problems were worth the want a portable that complements convenience of machine-readable my desktop system. It will use voice, notes, so I still use pen and paper, a pen/display, and perhaps o. cam­ but it is a close call between the two era for input and output. Storage and others might argue for its mer­ will probably be nonrotating, and it will be able to receive wireless com­ its. An alternative is to buy a pre­ munication. Most important, it will vious-generation portable. Con­ be part of a system that includes a sider, for instance, the Texas In­ desktop computer and local- and struments Travelmate 2000. (The wide-area networks. These systems Sharp PC-6220 and the Com­ must be designed to work together, puAdd Companion are identical). with functions placed on the appro­ A few years ago, this was the hottest priate machine. This integration is thing in portables, with a 1 2 M H z illustrated by some of the following 80286, I t o 3MB of memory and a 2The vision of a professional communication 20MB or 40MB hard disk. I t is 3 1 % medium is older than Kay's Dynabook. It slower than the Zeos on non-float dates to Vannevar Bush's 1 945 article [2] speculating on a hypothetical machine to help benchmarks, 44% slower on floating with his scientific reading, writing, and com­ point, and the disk is 85% slower. munication.

26

examples of system utilization. I write many notes-at lectures, meetings, and the gym . M y notetaking medium i s pen on 8 1/2 x I r sheets of paper. It is an excellent recording medium, well­ suited for text and sketches. It is terrible, however, for storage and retrieval. Most of these sheets of paper make it back to my office, where they are sorted into various files and piles, and I am afraid few are ever seen again. This is where the desktop system comes into play. It will be the data­ base machine that stores and re­ trieves notes taken on the portable, making them part of a lifelong, professional Dynabase. It will also do handwriting and voice recogni­ tion on many of the notes. It will be many years before a portable com­ puter comes close to the conven­ ience of paper for recording notes. I will switch to a portable before that because of the tools running on my desktop computer. I also use sheets of paper for de­ signing things such as CACM col­ umns, programs, courses, talks, or house floor plans. These are similar to the other notes, but are more likely to use varying data types like paint-images, draw-images, tables, spreadsheets, symbolic and nu­ meric equations, and outlines. A portable computer should have dif­ ferent types of "paper" for differ­ ent types of data, and the desktop machine should know about them too. While I use a lot of 8 1/2 x 1 1 paper, my favorite note-taking medium is in the margins of books and articles. Sad to say, these notes are even less likely to be retrieved. Writing-while-reading is a very important application. Perhaps the best measure of the value of a book is the number of marginal notes scrawled on it-reading is conver­ sation. Slate Corporation has an­ nounced Pen Book, a program that appears to be suited to this applica­ tion. Books are portable and easy on the eyes, but I would be willing to

March 1992 /Vol.35, No.3/COMMUNICATIONS OF THE ACM

PC trade some of those advantages for the ability to capture marginal notes, and add them to my Dynabase. Marginal notes would be stored along with lecture and de­ sign notes, and they would be asso­ ciated with the relevant document and scanned excerpts. They can also be electronically mailed to the author, closing the reading-as­ conversation loop. Since we increasingly read elec­ tronic as opposed to printed mate­ rial, a portable computer also needs enough storage to carry significant chunks of the desktop away from the office. For example, I would like to leave the office with a copy of a book or a paper and all the papers to which it refers. Sony's Data Diskman foreshadows this capability, but it is limited by its use of CD-ROM media. I see the portable as a dynamic inputloutput medium used in con­ junction with a desktop machine that will maintain the Dynabase. Because of its unique capabilities, the portable will also often be used in the office. Finally, information from other sources such as net­ works or CD-ROM will also be stored in the Dynabase. The Technology

It will take many years to get a sys­ tem such as the one just described, but we can look at what is available today and in the near future. There are several technologies underlying the portable, but the hard part is not the portable; it is the Dynabase. The portable will have an inte­ grated digitizer-display for pen inputloutput. Pen-based computers have been available for several years with little impact, but interest in them is high. Yourdon [8] states "I have seen the future and it is spelled P-E-N." He feels we are in "the formative stages of a new era in computing: the age of pen com­ puting. Approximately a dozen companies showed pen-based products or prototypes at Comdex this year. There are major system software efforts at GO and Micro-

COMMUNICATIONS OF THE ACM/March 1992/Vol.35, No.3

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Table , _

Desktop and Portable Benchmarks (B + {L}) and ({L} + C) ---'> D infer (A U C) ---'> (B U D). We can make a cut inference from two clauses if any only if there is some atom L which is in the ante­ cedent of one clause and the conse­ quent of the other. To form the conclusion of the inference, we first 'cut' out L from both places, and then merge the two antecedents into one and two consequents into one. The 'disjoint union' notation X + Y denotes the union X U Y, but also carries the further infor­ mation that x n y = 0. Example I. From the clauses A B ---'> C D and D E ---'> F G we can infer the clause A B E ---'> C F G by a

cut, eliminating the atom D. The resolution inference pattern generalizes the cut inference pat­ tern by bringing in unification. The resolution inference pattern has the form : from

A -'> (B + M) and (N + C) ---'> D (A U C)u ---'> (B U D)u infer where u is an mgu of the one­ part partition {M U N}.

{F(F(F(F(F(F(F(F(x)))))))), F(F(F(F(F(F(F( F(A))))))))} we can merge only one pair of nodes, and generate only one new link, at each iteration of the loop. These successive minimal modifica­ tions of the graph therefore com­ prise essentially a sequential pro­ cess. However, such 'worst cases' are more pathological than typical, and experience suggests that they are rarely met in real applications. Resolution

Once we can compute an mgu for any unifiable partition of a set of expressions (or show the partition not to be unifiable, if that is the

In making a resolution inference, we must first use unification to de­ duce a pair of instances of the two premises suitable for a cut to be applied. In the special case that M = N = {L}, the mgu of the parti­ tion {M U N} is the identity substi­ tution. So in this case, a resolution is the same as a cut. Example 2 . From ---'> P (G(r s) r s) and P(x y u)P(y z v)P(x v w) ---'> P(u z w) we infer P(r z r) ---'> P(s z s) by a resolution in which M = {P(G(r s) r

COMMUNICATIONS OF THE ACM/March 1992/Vol.35. No.3

s)} and N = {P(x y u) ,P(x v w)}, since {M U N} is unifiable with mgu {x = G(r s), y = v = r, u = w = s}.

Example 3 . From P(x y u)P(y z

v)P(x v w) ---'> P(u z w) and P(a b c)P(b d e)P(c d f) ---'> P(a e f) we infer P(x y a)P(y b v)P(x v c)P(b d e)P(c d f) ---'> P(a e f) by a resolution in which M = {P(u z w)} and N = {P(a b c)}, since {M U N} is unifiable with mgu {u = a, z = b, w = c}. From two given clauses, only a fi­ nite number of clauses can be in­ ferred by resolution-one for each choice of the 'cut' sets M and N for which the partition {M U N} is uni­ fiable. If there are no such choices of M and N, then nothing can be inferred from the two clauses by resolution. Resolution Deductions and Proofs

A resolution deduction is a finite tree whose nodes are labeled by clauses, each nonleaf node being labeled by a clause which is inferred by a reso­ lution inference from the clauses labeling its immediate successors. The conclusion of the deduction is the clause labeling its root, and the premises of the deduction are the clauses labeling its leaves. A resolu­ tion proof_ is a resolution deduction whose conclusion is false ( = the empty clause). Such a proof estab­ lishes that the premises are contra­ dictory (unsatisfiable). If S is any unsatisfiable set of clauses there is always a resolution proof whose premises are all in S. This fact is the completeness of resolution (see [39]. A resolution proof with n + 1 premises can be taken in n + 1 dif­ ferent ways as a proof of the nega­ tion of one of its premises from the other n premises. For example, a resolution proof with premises A , B , C can be taken as ( 1 ) a proof of not-A from the premises B and C, (2) a proof of not-B from the prem­ ises A and C, and (3) a proof of not-C from the premises A and B. P1 - Resolution

A resolution one of whose two premises

51

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Logic Programming is unconditional is called a PI -resolu­ tion. Example 2 is a P i -resolution,

Hyperresolution Deductions

A hyperresolution deduction is a fi­ but Example 3 is not. It turns out nite tree each of whose nodes has a that whenever a set of clauses is label and each of whose nonleaf unsatisfiable, then there is a P l ­ nodes also has a justification. The resolution proof from those prem­ labels are unconditional clauses, and ises (see [ 40]). In other words, P l ­ the justifications are conditional resolution is also complete: despite clauses. The clause labeling a non­ its restricted form, P I -resolution is leaf node N is inferred by a hyper­ j ust as strong as resolution, but its resolution whose unconditional proof-space is sparser than that of premises are the clauses labeling the immediate successors of N, and unrestricted resolution. whose conditional premise is the justification of N. The conclusion of Hyper-Resolution We get an even sparser proof-space the deduction is the clause labeling when we take as the only inference its root. The premises of the deduc­ rule, instead of the two-premise P l ­ tion are the labels of its leaf nodes resolution, the (p + l )-premise and the justifications of its nonleaf hyper-resolution rule in which exactly nodes. H yperresolution deductions can one of the premises is a conditional clause and all of the other p prem­ yield only unconditional clauses. ises, together with the conclusion, are Moreover, they can yield only posi­ unconditional clauses. The hyper­ tive unconditional clauses, unless the resolution rule is: justification of the root node is a nega-(C 1 + M 1) , . . . , (Cp + Mp), and N 1 + · · · + Np - D infer -(C 1 U· · · U C P U D)a where a is an mgu of the p-part partition {M 1 U N 1 , . . . , Mp U Np} ·

from

The unifiable p-part partition that is the essential ingredient of a hy­ perresolution is called its kernel. The p + l premises and the kernel together uniquely determine the conclusion. A hyperresolution inference is really a compacted reorganization of a P I -resolution deduction whose conclusion is unconditional. After the reorganization the deduction has had all of its interior nodes sup­ pressed and has become a single integrated transaction instead of a linked system of many transactions. By reorganizing the reasoning as a single inference, we are simply re­ garding its conclusion as having been obtained directly (or, to use a traditional logic expression, immedi­ ately -without any 'mediation') from its premises in one step, rather than 'mediately' as the even­ tual outcome of several linked P l ­ resolution steps.

56

tive conditional clause and in that

case, but only in that case, the con­ clusion is a negative unconditional clause; indeed, it is the empty clause. Thus a hyperresolution deduction of the empty clause (a hyperresolution proof) always has exactly one negative conditional clause

among its justifications. As we shall see, it is this feature which adum­ brates logic programming. Completeness and Local Finiteness of the Resolution Clausal Predicate Calculi

The resolution and hyperresolu­ tion versions of the clausal predi­ cate calculus are all complete. Also, both systems are locally finite. This means that, in each system, there are only finitely many deductions of a given size (number of nodes) having a given set of premises (and this number is much smaller for hyperresolution than for resolu­ tion). By contrast, traditional predi­ cate calculi are not even locally fi-

nite. This is one reason it is so difficult to make an efficient proof procedure for tradilional predicate calculi. For example, most tradi­ tional predicate calculi contain the rule of specialization: from '\;/A infer '\:/(AO) , where () is any substitution.

(The sentence VS is the universal closure of the sentence S : the result of prefixing a universal quantifier to S for every free variable in S). With this inference available, there are infinitely many deductions of size 2 which have the same premise '\;/A-one for each different substi­ tution e. Hyperresolution and Horn Clause Logic

The advantages of hyperresolution are quite striking in the Horn clause predicate calculus. In this subsystem of the clausal predicate calculus every clause is a Horn clause, namely, a clause having at most one conclusion. Hyperresolution then becomes much simpler. Recall the general definition of hyper­ resolution : -(C 1 + M 1 ) , . . . , + Np - D (Cp + Mp), and N 1 + infer -(C 1 U · · U Cp U D)a , where a is an mgu of the p-part partition {M 1 U N 1 ; . ., Mp U Np} · from

· · ·

·

When all clauses are restricted to having at most one conclusion, the 'cut' sets Mi can only be singletons (say, {AJ) , and the 'remainder' sets Ci must be empty. Consequently, the definition of hyperresolutions for Horn clauses can be restated, in the following much simpler form: from

-A l > . . . , -A p , {B 1 , . . . , B p} - D

infer -Da where a is an mgu of the p-part

partition {{A1 , B 1 } , . . . , {Ap, B p}}

In this restatement of the rule, D and the A's and B's are all atomic sentences. When we combine hy­ perresolution inferences into mul­ tiinference deductions, we are in effect treating each particular ap­ plication of this inference pattern

March 1992 /Vol.35, No.3/COMMUNICATIONS OF THE ACM

·

as though it were a special infer­ ence rule, 'the {B 1 , . . . , B p} -? D inference rule', stated as:

has the same premise and the same conclusion as D, and conversely. We define ultraresolution inferences

from -7A 1 , . . . , -?A r infer -? Du where u is an mgu of the p-part

partition {{A l > B 1}, . . . , {Ap , B p}}. This is, however, just a pragmatic device to sharpen our understand­ ing of the very special role that con­ ditional Horn clauses play in logic programming. U ltraresol utions: Horn Clause Hyperresolution Deductions as Single Inferences

We again apply the idea of making a single inference out of an entire deduction. In the case of hyper­ resolution, instead of thinking of the conclusion of an entire deduc­ tion (namely a deduction built from P I -resolution steps and having an unconditional conclusion) as being arrived at stepwise by the perfor­ mance of each of its inferences sep­ arately, we think of the whole con­ struction as one inference step involving a higher and larger-scale inference pattern. We will now treat Horn clause hyperresolution de­ ductions in a similar way, and thereby arrive at a higher- and larger-scale inference pattern which we call ultraresolution. There is really no need, prag­ matically, to know the conclusion of every individual inference in a hy­ perresolution deduction, if all that we are after is the eventual conclu­ sion of the whole deduction. We can instead characterize that even­ tual conclusion more directly, by a relationship based only on the structure of the premises of the deduction. By omitting in this way all of the interior stepwise conclu­ sions we turn the entire hyper­ resolution deduction into a single in­ ference, which immediately yields its conclusion from the premises in one integrated step.

is a cover of A(xo) B(xo) -? C(xo) by C, in view of the assignments given by the table: atom

assigned to node

A(xo) B(xo) H(G(x2)) D(x 1 Y 1 ) E(x 1 )

2 3 4 5 6

directly, however, without refer­ ence to their corresponding hyperresolution deductions. and has the following partition as The ultraresolution rule is its kernel : (where A -? B is a Horn-clause and C is a set of Horn-clauses): from A -? B and C infer -?Bu if there is a cover of A -? B by C whose kernel is unifiable with mgu u. The clause A -? B is the main prem­ {{A(xo), A(F(x 1 Y 1 ))} , {B(xo, B(x2)}, ise and the clauses in C are the cov­ {E(x1 ) , E(M)}, {D(x y 1 ) , D(M N)}, 1 ering premises. {H(G(x2)), H (G(x3 ))}. covers and Their Kernels

A cover of a clause A -7 B by a set C of clauses is a certain kind of finite tree with nodes labeled by clauses. The root of the tree is labeled by A -? B, while the other nodes are labeled by variants of clauses in C. The extra condition that makes the tree a cover is that for each node N in the tree, every atom in the ante­ cedent of the clause labeling N is assigned to a distinct immediate successor of N. The kernel of the cover is the partition : {{X, Y}IY i s the conclusion o f the clause labelling the node to which X is assigned}. Example 4. To illustrate the no­ tions of a cover and its kernel, con­ sider the clause: A(xo) B (xo) -? C(xo) and the set C of clauses {E(xi ) D(x 1 Y 1 ) -7 A(F(x 1 Y 1 )), H (G(x2)) -7 B(x2 ) , -7 H (G(x3 )), -7 D( M N) , -7 E(M)}. The labeled tree given by the table: node parent

Ultra resolution

To every hyperresolution deduc­ tion D there corresponds an ultraresolution inference U which

COMMUNICATIONS O F T H E ACM/March 1992/Vol .35. No.3

I 2 3 4 5 6

I

I 3 2 2

Since this kernel is unifiable, with mgu u = {xo = x2 = X 3 X 1 = M, Y 1 = N},

=

F(M N)),

we can infer the clause -7C(x0)u = -?C(F(M N))

by an ultraresolution which has A(x0) B(xo) -? C(xo) as its main premise and C as its set of covering premises. The intuition behind the notion of a cover of a clause A -? B is that it depicts exactly the pattern of orga­ nization of the given clauses. If the kernel of the cover is unifiable with mgu u, it guarantees that we can easily relabel the tree so it turns into a hyperresolution deduction, from these clauses as premises, of the same unconditional clause -?Bu that the ultraresolution inference obtains directly from them in one step. In this relabeling, the new label on each leaf node of the tree is the same as the old label. The old

label A(xo) B (xo) -? C(xo) E(x 1 ) D(x 1 Y 1 ) -7 A(F(x 1 Y 1 )) H(G(x2)) -7 B (x2) -7 H(G(x3 )) -?D(M N), -?E(M)

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Logic Programm ing --

label on each nonleaf node of the cover, however, is removed (it now becomes the justification of the hy­ perresolution inference at that same node), and the node's new label is the unconditional clause which is inferred by a hyperresolu­ tion from this j ustification clause together with the new labels on the immediate successors of the node. The following example illustrates the relationship between a hyperresolution deduction and the corresponding ultraresolution inference.

41 (2)

37

40

Example 5. Figure 6 is a hyper­

resolution deduction of the uncon­ U NCLE(TED clause ditional ANN)- from a subset of the fol­ lowing set of Horn clauses, which comprises a small 'family relation­ ship' knowledge base. This knowl­ edge base contains (as its 'defini­ tions') the following conditional Horn clauses: 1 2 3 4 5 6 7 8 9 10

UNCLE(u x) U NCLE(u x) PARENT(x,y) B ROTHER(b x) SISTER(s x) SIBLI NG(x y) H USBAND(h w) WIFE(w h) FATHER(f x) MOTHER(m x)

FIGURE 6.

-BROTHER(u y) PARENT(y x) -HUSBAND(u s) SISTER(s p) PARENT(p x) -cH ILD(y,x) -SIBLING(b x) MALE(b) -srnLING(s x) FEMALE(s) -DI FFERENT(x y) FATHER(f x) FATHER(f y) MOTHER(m x) MOTHER(m y) -MA RRIED(h w) MALE(h) -MA RRIED(h w) FEMALE (w) -PARENT(f x) MALE(f) -PA RENT(m x) FEMALE(m)

and (as its 'facts') the following un­ conditional Horn-clauses: 11 12 13 14

C H I LD(JIM JOE)C H I LD(JOE MEG)CHILD(JIM SUE)C H I LD(ANN JOE)-

15 16 17 18

C H ILD(JOE TOM)- 1 9 CHI LD(TOD PAT)C H I LD(AN N SUE)- 20 CHILD(RON PAT)C H I LD(PAT MEG)- 2 1 CHILD(TOD TED)C H ILD(PAT TOM)- 22 CHILD(RON TED)-

23 24 25 26 27

MALE(J IM)MALE(JOE)MALE(TOM)MALE(TED)MALE(TOD)-

29 30 31 32 33

FEMALE(ANN)FEMALE(SUE)FEMALE(MEG)FEMALE(PAT)FEMALE(SAL)-

40 D IFFERENT(a b)- a ¥- b & a, b,

E

35 36 37 38 39

MARRIED(TOM MEG)MARRIED(JOE SUE)MARRIED(TED PAT)MARRI ED(RON SAL)MARRIED( J IM JAN)-

{JIM, JOE, TOM, TED, TOD, RON , ANN, SUE, MEG, PAT, SAL, JAN}

Premise 40 is a 'virtual' definition: it is simply a shorthand way of sup­ plying 1 32 facts (such as D I F­ FERENT(JOE A N N)-) whose predicate is DIFFERENT and whose two arguments are distinct constants in the displayed set.

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From this knowledge base there are, for example, hyperresolution deductions of each of the following unconditional clauses: 41 42 43 44

U NCLE(TED ANN)