132 RESPONSE

On Logical Foundations of Artificial Intelligence, a response to the reviews by S. Smoliar and J. Sowa

Response by: Nils Nilsson Department of Computer Science, Stanford University, Stanford, CA 94305, U.S.A.

I found the reviews of Logical Foundations of Artificial Intelligence by John Sowa and by Stephen Smoliar to be both helpful and perceptive. One cannot disagree with their suggestions to add more examples, to explain certain concepts in more detail with more examples, to add more descriptive material in the bibliographic notes, and to fix the typos. Now that the anxiety of meeting a publishing deadline is past and we can look at our work more dispassionately, we might even agree with the reviewers on certain pedagogic matters such as the need for more material about Kripke semantics and its role in reasoning about necessity and possibility before plunging into the knowledge operator . These reviews will be very helpful when (and if) we decide to write a second edition. (A second printing has already corrected the typographical errors known to us at the time of printing.)

The reviewers do raise several points however, about which AI researchers can disagree. We appreciate the opportunity to mention some of these matters here.

Both reviewers compliment us on presenting the logical foundations of AI but complain that we should have also tried to make a bet ter case for why logic in general (and our t reatment of it in particular) is foundational. They would have liked to have seen us describe how these methods might be useful in large, practical problems. To a certain extent, I suppose we assume in the book that most serious AI researchers have already agreed that logic is foundat ional-- leaving it to other authors (or ourselves in other circumstances) to argue the case. In fact, we think the case has already been made. One can look at AAA1 Proceedings and IJCA1 Proceedings over the past several years to see the trend: more and more articles are not even readable unless one is familiar with concepts like logical formulas, inference, nonmonotonic reason- ing, models, quantification, unification, metalevel reasoning and the like. Knowledge about these subjects is part of the technical apparatus that all AI researchers need to have.

Our approach, we suppose, is something like that taken by authors of a text on calculus. The vocabulary, concepts, and techniques are presented; practice is provided through exercises such as computing the volume of a cylinder, but not much mention is made (nor needs to be made) of how calculus is used to help design moon rockets. Similarly, we felt that our task was to present and

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explain the logical ideas that we observe our colleagues and ourselves using as they talk about complex AI applications. To connect these fundamental ideas with the applications themselves is best done not in a textbook but in a casebook. Casebooks are particular to the field of applications studied and are vastly more dependent on current implementational technology.

We disagree with Sowa and with Smoliar about certain topics that one or both of them wanted us to include or emphasize more in the book:

(1) Should have more on default theories. The tide of work now seems to be shifting to circumscription and away from default theories. (Reiter even seems to acknowledge that in a recent Annual Reviews survey on nonmonotonic reasoning.)

(2) Should include something on fuzzy logic and Dempster -Shafer treat- ments of uncertainty. We regard these techniques as temporary idiosyncracies.

(3) Should have more on PROLOG. We regard PROLOG as a computer language just as LISP is a computer language. There is no necessary commit- ment to PROLOG by people taking a logical approch to AI. One can program up the most ad hoc and specialized systems using PROLOG--just as one can (indeed, does) build elegant, theorem-proving systems in LISP. True, (pure) PROLOG does use what we call depth-first, backward directed, ordered resolu- tion on Horn clauses. Perhaps we should have stressed that fact more. We might also have tied in some of the material presented in Chapter 10 with PROLOG.

(4) Should have included material on truth maintenance. Perhaps. It seemed to us a family of rather simple bookkeeping operations on derivations to save computation in case belief sets are changed. We'll consider including material on this subject in the next edition. (In the same category, we might have included some material on connection graphs and their use in theorem proving.)

(5) Should have acknowledged the role of nonresolution (say, natural deduction) theorem proving. Perhaps. Most of these methods can profitably be converted to resolution methods, and, in any case, the vocabulary and tech- niques that come along so easily with resolution (such as unification) are fundamental to all computationally practical theorem-proving techniques.

Neither reviewer mentioned what we regard as a serious omission, namely the subject of reasoning about time. In fact, a draft chapter fought its way into various stages of completion but neither of us could decide that it really was complete. So, alas, it must await the next edition. Another edition should also have a much expanded treatment on semantic attachment (h la Richard Weyhrauch).

We thank the reviewers for their careful reading of our book and for their comment.