Logic, Math and AI
In many ways the great quest of Doug Lenat’s life was an attempt to follow on directly from the work of Aristotle and Leibniz. For what Doug was fundamentally trying to do over the forty years he spent developing his CYC system was to use the framework of logic—in more or less the same form that Aristotle and Leibniz had it—to capture what happens in the world. It was a noble effort and an impressive example of long-term intellectual tenacity. And while I never managed to actually use CYC myself, I consider it a magnificent experiment—that if nothing else ultimately served to demonstrate the importance of building frameworks beyond logic alone in usefully representing and reasoning about the world.
Doug Lenat started working on artificial intelligence at a time when nobody really knew what might be possible—or even easy—to do. Was AI (whatever that might mean) just a clever algorithm—or a new type of computer—away? Or was it all just an “engineering problem” that simply required pulling together a bigger and better “expert system”? There was all sorts of mystery—and quite a lot of hocus pocus—around AI. Did the demo one was seeing actually prove something, or was it really just a trivial (if perhaps unwitting) cheat?
I first met Doug Lenat at the beginning of the 1980s. I had just developed my SMP (“Symbolic Manipulation Program”) system, that was the forerunner of Mathematica and the modern Wolfram Language. And I had been quite exposed to commercial efforts to “do AI” (and indeed our VCs had even pushed my first company to take on the dubious name “Inference Corporation”, complete with a “=>” logo). And I have to say that when I first met Doug I was quite dismissive. He told me he had a program (that he called “AM” for “Automated Mathematician”, and that had been the subject of his Stanford CS PhD thesis) that could discover—and in fact had discovered—nontrivial mathematical theorems.
“What theorems?” I asked. “What did you put in? What did you get out?” I suppose to many people the concept of searching for theorems would have seemed like something remarkable, and immediately exciting. But not only had I myself just built a system for systematically representing mathematics in computational form, I had also been enumerating large collections of simple programs like cellular automata. I poked at what Doug said he’d done, and came away unconvinced. Right around the same time I happened to be visiting a leading university AI group, who told me they had a system for translating stories from Spanish into English. “Can I try it?” I asked, suspending for a moment my feeling that this sounded like science fiction. “I don’t really know Spanish”, I said, “Can I start with just a few words?” “No”, they said, “the system works only with stories.” “How long does a story have to be?” I asked. “Actually it has to be a particular kind of story”, they said. “What kind?” I asked. There were a few more iterations, but eventually it came out: the “system” translated one particular story from Spanish into English! I’m not sure if my response included an expletive, but I wondered what kind of science, technology, or anything else this was supposed to be. And when Doug told me about his “Automated Mathematician”, this was the kind of thing I was afraid I was going to find.
Years later, I might say, I think there’s something AM could have been trying to do that’s valid, and interesting, if not obviously possible. Given a particular axiom system it’s easy to mechanically generate infinite collections of “true theorems”—that in effect fill metamathematical space. But now the question is: which of these theorems will human mathematicians find “interesting”? It’s not clear how much of the answer has to do with the “social history of mathematics”, and how much is more about “abstract principles”. I’ve been studying this quite a bit in recent years (not least because I think it could be useful in practice)—and have some rather deep conclusions about its relation to the nature of mathematics. But I now do wonder to what extent Doug’s work from all those years ago might (or might not) contain heuristics that would be worth trying to pursue even now.
I ran into Doug quite a few times in the early to mid-1980s, both around a company called Thinking Machines (to which I was a consultant) and at various events that somehow touched on AI. There was a fairly small and somewhat fragmented AI community in those days, with the academic part in the US concentrated around MIT, Stanford and CMU. I had the impression that Doug was never quite at the center of that community, but was somehow nevertheless a “notable member”, who—particularly with his work being connected to math—was seen as “doing upscale things” around AI.
In 1984 I wrote an article for a special issue of Scientific American on “computer software” (yes, software was trendy then). My article was entitled “Computer Software in Science and Mathematics”, and the very next article was by Doug, entitled “Computer Software for Intelligent Systems”. The summary at the top of my article read: “Computation offers a new means of describing and investigating scientific and mathematical systems. Simulation by computer may be the only way to predict how certain complicated systems evolve.” And the summary for Doug’s article read: “The key to intelligent problem solving lies in reducing the random search for solutions. To do so intelligent computer programs must tap the same underlying ‘sources of power’ as human beings”. And I suppose in many ways both of us spent most of our next four decades essentially trying to fill out the promise of these summaries.
A key point in Doug’s article—with which I wholeheartedly agree—is that to create something one can usefully identify as “AI”, it’s essential to somehow have lots of knowledge of the world built in. But how should that be done? How should the knowledge be encoded? And how should it be used?
Doug’s article in Scientific American illustrated his basic idea:
Encode knowledge about the world in the form of statements of logic. Then find ways to piece together these statements to derive conclusions. It was, in a sense, a very classic approach to formalizing the world—and one that would at least in concept be familiar to Aristotle and Leibniz. Of course it was now using computers—both as a way to store the logical statements, and as a way to find inferences from them.
At first, I think Doug felt the main problem was how to “search for correct inferences”. Given a whole collection of logical statements, he was asking how these could be knitted together to answer some particular question. In essence it was just like mathematical theorem proving: how could one knit together axioms to make a proof of a particular theorem? And especially with the computers and algorithms of the time, this seemed like a daunting problem in almost any realistic case.
But then how did humans ever manage to do it? What Doug imagined was that the critical element was heuristics: strategies for guessing how one might “jump ahead” and not have to do the kind of painstaking searches that systematic methods seemed to imply would be needed. Doug developed a system he called EURISKO that implemented a range of heuristics—that Doug expected could be used not only for math, but basically for anything, or at least anything where human-like thinking was effective. And, yes, EURISKO included not only heuristics, but also at least some kinds of heuristics for making new heuristics, etc.
But OK, so Doug imagined that EURISKO could be used to “reason about” anything. So if it had the kind of knowledge humans do, then—Doug believed—it should be able to reason just like humans. In other words, it should be able to deliver some kind of “genuine artificial intelligence” capable of matching human thinking.
There were all sorts of specific domains of knowledge to consider. But Doug particularly wanted to push in what seemed like the most broadly impactful direction—and tackle the problem of commonsense knowledge and commonsense reasoning. And so it was that Doug began what would become a lifelong project to encode as much knowledge as possible in the form of statements of logic.
In 1984 Doug’s project—now named CYC—became a flagship part of MCC (Microelectronics and Computer Technology Corporation) in Austin, TX—an industry-government consortium that had just been created to counter the perceived threat from the Japanese “Fifth Generation Computer Project”, that had shocked the US research establishment by putting immense resources into “solving AI” (and was actually emphasizing many of the same underlying rule-based techniques as Doug). And at MCC Doug had the resources to hire scores of people to embark on what was expected to be a few thousand person-years of effort.
I didn’t hear much about CYC for quite a while, though shortly after Mathematica was released in 1988 Marvin Minsky mused to me about how it seemed like we were doing for math-like knowledge what CYC was hoping to do for commonsense knowledge. I think Marvin wasn’t convinced that Doug had the technical parts of CYC right (and, yes, they weren’t using Marvin’s theories as much as they might). But in those years Marvin seemed to feel that CYC was one of the few AI projects going on that actually made any sense. And indeed in my archives I find a rather charming email from Marvin in 1992, attaching a draft of a science fiction novel (entitled The Turing Option) that he was writing with Harry Harrison, which contained mention of CYC:
June 19, 2024
When Brian and Ben reached the lab, the computer was running
but the tree-robot was folded and motionless. “Robin,
“Robin will have to use different concepts of progress for
different kinds of problems. And different kinds of subgoals
for reducing those different kinds of differences.”
“Won’t that require enormous amounts of knowledge?”
“It will indeed—and that’s one reason human education takes
so long. But Robin should already contain a massive amount of
just that kind of information—as part of his CYC-9 knowledge-
“There now exists a procedural model for the behavior of a
human individual, based on the prototype human described in
section 6.001 of the CYC-9 knowledge base. Now customizing
parameters on the basis of the example person Brian Delaney
described in the employment, health, and security records of
A brief silence ensued. Then the voice continued.
“The Delaney model is judged as incomplete as compared to those
of other persons such as President Abraham Lincoln, who has
3596.6 megabytes of descriptive text, or Commander James
Bond, who has 16.9 megabytes.”
Later, one of the novel’s characters observes: “Even if we started with nothing but the
old Lenat–Haase representation-languages, we’d still be far ahead of what any animal ever evolved.” (Ken Haase was a student of Marvin’s who critiqued and extended Doug’s work on heuristics.)
I was exposed to CYC again in 1996 in connection with a book called HAL’s Legacy—to which both Doug and I contributed—published in honor of the fictional birthday of the AI in the movie 2001. But mostly AI as a whole was in the doldrums, and almost nobody seemed to be taking it seriously. Sometimes I would hear murmurs about CYC, mostly from government and military contacts. Among academics, Doug would occasionally come up, but rather cruelly he was most notable for his name being used for a unit of “bogosity”—the lenat—of which it was said that “Like the farad it is considered far too large a unit for practical use, so bogosity is usually expressed in microlenats”.
Doug Meets Wolfram|Alpha
Many years passed. I certainly hadn’t forgotten Doug, or CYC. And a few times people suggested connecting CYC in some way to our technology. But nothing ever happened. Then in the spring of 2009 we were nearing the first release of Wolfram|Alpha, and it seemed like I finally had something that I might meaningfully be able to talk to Doug about.
I sent a rather tentative email:
some of your interests.
I just made a small blog post about it:
I’d be pleased to give you a webconference demo if you’re interested.
I hope you’ve been well all these years.