Journal of Automated Reasoning 9: 409-411, 1992. 409

Book Review

L6a Somb& Reasoning under Incomplete Information in Artificial Intelligence, John Wiley & Sons, New York, 1990, 150 pp. $39.80.

Any reasoning system that attempts to deal with real-world problems must face the problem of reasoning with incomplete information, Systems have finite knowledge bases and thus cannot be equipped with every fact that they will ever need. Thus they must be furnished with means of inferring the necessary information by, say, deter- mining the characteristics of a particular object from information about other mem- bers of the class of objects of which it is a member. The importance of equipping

systems with formal methods to deal with these problems has long been recognized, and a large array of different techniques has been developed to handle incomplete information.

One of the unfortunate consequences of this proliferation of techniques is that,

because they were developed in different laboratories to solve different aspects of the 'incompleteness problem' in different ways, there are considerable differences between

them. This is not surprising, but it does mean that the similarities between the techniques, which are to be expected given that they are addressing the same problem, are masked by a confusing profusion of terms and symbols which are impenetrable

to all but the most determined specialists. Or, at least, they were before the publication of L~a Somb6's Reasoning under

Incomplete Information in Artificial Intelligence. L6a Somb6 is the nora de plume of a group of top French workers in automated

reasoning who have assembled probably the most complete survey of logical techni- ques for tackling the problem of incompleteness yet compiled. The 275 references alone testify to the magnitude of the achievement, but this is not the most important aspect of the work, for the book offers something completely new, and far more useful. Each of the methods described is discussed with reference to a single example - - the representation of a series of facts of the form ~The As are Bs'*, and the answering of a number of queries based on reasoning from the facts. The fact that a concrete, if not particularly complex, example is used has important ramifications. Not only is it possible to see how each formalism may be used, but a series of criteria for comparison of the formalisms is drawn up with reference to the example, and used to determine the pros and cons of each approach.

Both of these results are of great importance. As mentioned above, the mass of formalisms that have been introduced is confusing even to the specialist, let alone the

*The name L6a Somb6 derives from 'Les A sont B', the French for "The As are Bs'.

410 BOOK REVIEW

novice. As a result, anyone wishing to build a reasoning system that dealt with incompleteness before this book was written would have had to scratch around digging through the original papers on the subject such as Reiter (1980), McCarthy (1980), Moore (1985), dodging the heavy mathematics of the model and proof theories, to find that little or nothing had been written on how to represent knowledge more real than 'Typically birds fly'. Now, however, they can read the original ideas

served up in an easily digestible form* by L6a Somb6 and learn how to represent more complex ideas. Not only that, but because of the clever choice of the example, so that each formalism can model some parts of the problem but none can model all, the comparison criteria make it possible to judge how good a particular formalism will

be at handling a particular reasoning task. The comparison criteria also allow the reader to determine the relative usefulness

of the different formalisms. While other comparisons such as that carried out by Shoham (1987) have concentrated on highly technical aspects such as the preference

criterion used to select the preferred model, L~a Somb6 concentrates on more informal aspects such as whether there is more than one translation of the example into the formalism, whether the formalism is monotonic or not, and whether quantifiers like ~some' and 'most' may be represented. Once again, such comparisons are likely to be extremely useful to people who need to choose a formalism as the basis of a reasoning system but who don't wish to have to go into great detail about all the available formalisms in order to choose the most appropriate. Given a particular set of facts, one can quickly and simply assess the formalism, or formalisms, that best model the

knowledge. In addition, L6a Somb6 make a contribution to the ongoing debate on the relation-

ship between methods for reasoning with incomplete information. Whereas these nonstandard logics were once seen as alternatives, the accepted point of view is now that they are complementary, and this is borne out by L6a Somb6's results. No single formalism is capable of representing all the information in this relatively simple problem. Thus, it seems reasonable that the solution of any real problem will require the use of several formalisms in combination. While L6a Somb6 do not attempt to answer the question of how this should be done, they provide a powerful argument for its necessity in the 'tentative conclusion', pointing out that bridges between

formalisms have already been developed. I would not hesitate to recommend this book to anyone interested in automated

reasoning about real-world problems. Although there will always be hardline pragma- tists who will baulk at the idea of formal methods, the use of such methods seems to be widely accepted, and this is the best introductory text available, combining as it does a description of the best-known techniques, notes on their application, and the means to select the correct one for a particular application, In addition, for those with

*The book is extremely easy to read -- all praise to Sandra Sandri who did a remarkable job of translation, especmlly given that she is a native speaker of neither Enghsh nor French, and Bob Mercer who proofread parts of the manuscript.

BOOK REVIEW 4l 1

a more advanced knowledge o f the subject, it p rovide(s useful results on the quest ions

of to wha t extent the var ious formal reasoning me thods are c omp le me n ta ry and how

they may be used in combina t ion .

References

McCarthy, J. (1980) Circumscription - - a form of non-monotonic reasoning, Art~cial Intelligence 13, 27 39.

Moore, R. C. (1985) Semantical considerations on nonmonotonic logic, Artificial Intelligence 25, 75-94. Relter, R. (1980) A logic for default reasoning, Artificial Intelligence 13, 81-132. Shoham, Y. (1987) Nonmonotonic logics: Meaning and utility, Proc. IOth Internatwnal Joint Conference

on A1 (IJCAI 1987), Milan, Italy, pp. 388-393.

Queen Mar)' and Westfield College,

London, U.K.

S I M O N P A R S O N S