Review of Automated Reasoning: Thirty-Three Basic Research
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Book Reviews AI Magazine Volume 10 Number 3 (1989) (© AAAI) BookReviews Automated Reasoning: author writes with a freshness and an price of a (computer science) book is Thirty-Three Basic obvious love for logic. inversely proportional to its content. Between the listing of the prob- This book confirms this law: It is Research Problems lems and their detailed discussion is delightfully low priced. As Georg Ulrich Wend1 a review of AR. It seems to be too Christoph Lichtenberg, a German sketchy for the novice, but a com- physicist of the eighteenth century To read the book Automated Reason- panion book by the same author said: “If you have two trousers, sell ing: Thirty-Three Basic Research Prob- (Wos, L.; Overbeek, R.; Lusk, E.; and one, and buy this book.” lems (Prentice Hall, Englewood Cliffs, Boyle, J. 1984. Automated Reasoning: Ulrich Wend1 is at the SCS Information- N.J., 1987, 300 pp., $11.00) by Larry Introduction and Applications. Engle- stechnik GmbH, Hoerselbergstr. 3, 8000 Wos “it is not necessary to be an wood Cliffs, N.J.: Prentice-Hall.) gives Munchen 80. expert in mathematics or logic or far more details. computer science” (from the preface). Chapter 5, the in-depth discussion, However, even if you are such an is remarkable for its style. It is fasci- expert, you will read it with interest, nating to immerse oneself into the Logical Foundations of and likely, with enjoyment. details guided more by questions Artificial Intelligence The book is outstanding for its pre- from the author than answers; sentation of the theme. Following the indeed, a whole paragraph consists of Drew McDermott introductory chapter, Wos discusses nothing but questions! You will some obstacles to the automation of enjoy this chapter and the whole Knowledge is important to intelligent reasoning in Chapter 2. In Chapter 3, book, especially if you dislike the programs: Just about everyone in AI he lists the research problems (with ‘definition-theorem-proof’ style. The would agree, but the agreement short descriptions) in nine groups: six author’s presentation lets you forget doesn’t extend much further. There is problems on strategy, five on infer- that completely solving one of the a weak sense of “know” in which a ence rules, six on demodulation, one problems is considered equivalent to computer program knows P if its cor- on subsumption, three on knowledge finishing a Ph.D.! rectness depends on l? For instance, representation, two on global A non-expert will have the most an airline reservation system might approach, one on logic program- difficulty with the given test prob- “know” every passenger has a 0.9 ming, two on self-analysis, and six on lems primarily because they are all probability of showing up for a other areas. After a short review of out of the field of mathematics. reserved flight in the sense that it automated reasoning (AR) in Chapter Again, it is not trivial to see a corre- books 11 percent too many passen- 4, these problems are discussed in spondence to the problems or the gers. However, more interesting pos- detail in Chapter 5. Chapter 6 gives obstacles. At this point, it is likely the sibilities exist. A program might have some sets of test problems, all con- author’s opinion-“zeal, interest, and a notation that facts can be cerning a mathematical discipline. curiosity” suffice as prerequisites-is expressed, and it might consult a An appendix as interesting as the bib- too optimistic. However, this book is database of such facts to move liography follows. Last but not least also a workbook, and the appendix through problems. In this case, we there is an excellent index. shows the reader how to get the have a more explicit concept that a The discussion of the obstacles in appropriate software. Finally, besides program knows P if P is in the Chapter 2 is relaxing; although some a machine such as a VAX, you only database (or can be derived from it repetition exists in the book, the need one thing: a lot of time. Per- when required). This concept is the author spares you a puffy pseu- haps the best thing to say about the idea of declarative knowledge; the more dophilosophical treatise on AI in gen- book is that it tempted me to wait for mundane concept is called procedural eral and AR specifically. After reading a copy of the companion software. knowledge. The book Logical Founda- this chapter, you are convinced there The book as a whole is a rarity in tions of Artificial Intelligence (Morgan is no general problem solver, and you that it successfully serves several Kaufmann, Los Altos, Calif., 1987, have a pleasant introduction to the audiences at the same time. The 406 pp., $48.95) by Michael Gene- belly of the beast. layperson gets a real background sereth and Nils Nilsson is about the A non-expert might have some knowledge of one of the main disci- declarative version. (Declarative problems in mapping the eight obsta- plines of AI, and the theorist gets a knowledge could be false, and we cles described to the problems and good occasion to put the theory to would do better to call it belief, as I problem areas cited earlier. However, practice. Most astonishingly, both often do in this review.) the detailed discussion that forms the can enjoy it. Declarative knowledge requires a heart of the book provides the reader One last point is worth mention- notation, often called a knowledge with ample reward. It is clear that the ing. It seems to be a law that the representation system. Those who FALL I989 103 Book Reviews study declarative knowledge repre- concept learning, in which new rules warned that the foundations being sentations are divided about whether are inferred from facts that would explored are not exactly the founda- such notations ought to be thought follow from them. The algorithms tions of AI. of as variants of the predicate calcu- described-based on Tom Mitchell’s The authors’ viewpoint causes dis- lus and related systems of mathemat- idea of version spaces-are specific to tortions throughout the book. The ical logic invented by logicians, the domain of the concept of learn- chapter on planning (Chapter 12) is mathematicians, and philosophers in ing. Similarly, Chapter 8 describes typical. The planning problem is this century. Lately, those who think Bayesian inference, from a priori defined as finding a constructive they ought to be so regarded seem to probabilities to a posteriori probabili- proof that a series of actions will be winning. Genesereth and Nilsson ties given new evidence. bring about a desired state of the have no doubt and take it for granted In competition with this diversity world. It is assumed that the right that the semantic tools of mathemat- is the idea of a unified model of infer- way to find this proof is to tailor a ical logic are indispensable for ana- ence. The desire for such a model is general-purpose theorem prover with lyzing knowledge representations. strong among those who study a few specialized strategies. This They adopt the label Iogicism for this declarative representations, and description of the planning problem doctrine. Genesereth and Nilsson are no excep- is quite remote from any description In Chapter 2, they develop these tion. As are most of their colleagues, that active researchers in the field tools from the point of view of AI, they are drawn to the model of infer- would produce. Perhaps Genesereth which is rather different from the ence as the derivation of conclusions and Nilsson feel that techniques for logician’s point of view. They intro- that are entailed by a set of beliefs. solving planning problems will come duce the idea of conceptualization, They wander from this idea in a few and go, but the foundations can be which is roughly what a philosopher places but not for long. It is not hard secure. If so, they are too casual calls the intended model of a formal to see why: Deduction is one of the about the implicit claim. theory. A formal theory provides fews kinds of inference for which we I admit to bias on these questions. predicates and functions for talking have an interesting general theory. My skepticism should be balanced by about (some part of) the world and The authors made a conscious the agreement of many perfectly rea- axioms involving these symbols. decision not to talk much about sonable people with Genesereth and Formal semantics specifies a mapping search processes. Unfortunately, a Nilsson’s view. However, it bothers from the symbols to the entities in deductive process is always confront- me that questions about the scope of the world. It is one of the key ed with the problem of what to their enterprise are treated so superfi- insights (and disturbing insights) of deduce next; it is impossible to cor- cially in this book. mathematical logic that unique map- rectly choose with any confidence, so Let me put such doubts aside and pings are rare. Any given theory has programs that deduce must try vari- pretend from now on that deduction many interpretations that make its ous options. Sometimes, they can is the foundation of AI. Within this axioms true, that is, several models. generate many useless inferences perspective, the book has some Mathematicians cheerfully study before finding useful ones. Chapters strengths and some weaknesses. them all, but philosophers worry 4 and 5 are devoted to the topic of Chapter 6 is an excellent discussion more about how the correct model implementing deductive processes of nonmonotonic logic, a family of can be picked out.