Tracing chains-of-thought. Fuzzy methods in cognitive diagnosis (Q1382418)

This book is devoted to a study of cognitive processes associated with human reasoning, more specifically with problems of tutoring or guiding an inexperienced reasoner through the search space of concepts pertaining possibly to the problem in question in order to find a proper ``chain'' of concepts being the problem solution. Human reasoning in such situations is mostly of abductive character: it consists in inferring a plausible/probable explanation for a given set of facts. Formally, abduction conforms to an inference scheme of the form: \(\forall x\), \(\alpha_1 (x)\vee \dots \vee\alpha_k (x) \Rightarrow \beta(x)\), \(\beta(c)/ \alpha_i (c)\) i.e. from a given general rule \(\forall x\), \(\alpha_1 (x)\vee \dots \vee\alpha_k (x) \Rightarrow \beta (x)\) and a ground instance (fact) \(\beta (c)\), a plausible case \(\alpha_i (c)\) has to be hypothesized; various frameworks have been proposed for implementing this scheme like Parsimonious Set Covering \textit{J. A. Reggia}, \textit{S. Nau} and \textit{P. Y. Wang} [Inf. Sci. 37, 227-256 (1985; Zbl 0583.68046)]. Probability-based approach [cf. \textit{J. Pearl}, Probabilistic reasoning in intelligent systems: networks of plausible inference (1989; Zbl 0746.68089)]. Logic-based models [cf. \textit{H. Levesque}, IJCAI 89, Proc. Int. Conf., Detroit, MI/USA 1989, 1061-1067 (1989; Zbl 0713.68059)]. Activity Structure framework [cf. \textit{L. Kohout}, A Perspective on Intelligent Systems: A Framework for Analysis and Design (1990; Zbl 0723.68087)]. In this book the authors begin (in Part I) with an ontological discussion of the task of their project (Chapter 1), a general discussion of problems of tutoring in both human and machine environment (Chapter 2) and a chapter on problems of cognitive diagnosis where Parsimonius Set Covering and Activity Structure framework are presented (Chapter 3). A concept analysis, which underlies any treatment of cognitive diagnosis, involves in particular concept representing and evaluating closeness of concepts. The authors apply to this end fuzzy set theory proposed by Lotfi A. Zadeh. More specifically, they exploit fuzzy cognitive maps introduced by B. A. Juliano; they are introduced along with necessary prolegomena to fuzzy set theory in Part II (Chapter 4). In particular, measures of similarity or discrepancy of concepts represented as fuzzy cognitive maps are introduced (Defs. 4.24, 4.25). The core of the book is Part III where relational overlaps and discrepancies are studied on examples of some simple structures (Chapter 5) and Hasse diagrams derived from an urban environment perception data (Bandler and Mancini) are compared in terms of these measures. An important upshot of this study is the notion of a mapping between Hasse diagrams (Section 6.2) which is later (Chapter 7) generalized to a notion of a mapping between fuzzy cognitive maps. Examples are given of such mappings for many test structures. A culmination of this investigation is reached in Chapter 8 where the title notion of a chain-of-thought structure is presented based on the notion of a fuzzy cognitive map (as, informally, a finite-state sequential machine whose states are representing knowledge states modelled as fuzzy cognitive maps). Part IV brings an analysis of the proposed schemes in some frameworks (e.g. in Activity Structure framework) and a review of open problems. The book ends with Appendices where the reader may find among other things some examples of actual tutoring dialogues. The book will be interesting to researchers actively involved in problems of cognitive diagnosis as well as to researchers in fuzzy set theory who may find there many interesting points for a future investigation. The book is well-written however the reader not already well-versed in technicalities will have a slight difficulty in getting to the motivations and intuitions behind the introduced formalism as then authors concentrate on the technical aspects of the presented apparatus.