Logical structures for representation of knowledge and uncertainty
The book is an extensive study of the modifications theoretical logic should undergo if used in AI. There are two main arguments, to whose elaboration most of the text is devoted. The first one is that to a table of possible truth values of combinations of propositions, there should always be attached the probabilities or possibilities of the given outcome, either determined by a Bayesian hypothesis of equidistribution of all cases or on probabilistic reasoning. The second one is the remark that the well-known problems connected with the equivalence of \(A\to B\) and \(\neg A\vee B\), that give a value of ``true'' for \(A\to\neg A\), disappear in AI if the implication is used for queries since, in that case, \(A\) is always asserted, i.e., the only questions asked are of the type \(A\wedge (A\to B)\). In this context, a query \(A\wedge(\neg A\to B)\) is nonsensical. The implications of these theses for the use of two valued logic are studied in great detail in the first part; the second part then deals with the same subject where the truth value of a given proposition may be an indeterminate \(m\) in the interval \([0,1]\) or \((0,1)\). Here, the author refrains from going into computational rules of the composition of probabilities or possibilities, leaving her representation structure accessible to all theories of composition, whether probabilistic or fuzzy. A very short last part describes an AI system, written in LISP, developed by the author's students in their theses. It is unclear whether that system can be expanded to truly realistically large system working in reasonably short answer times.
scientific article; zbMATH DE number 1134728