Rezensionen
Rezensionen
Hermann Rodenhausen
Knowledge Description and Galois Correspondence
Practical Impact of a Structural Idea
Rezension
A developmenr of the so-called knowledge space theory in the domain of cognitive psychology goes back to J.-P. Doignon and J.-C. Falmagne. [Int. J. Man-Mach. Stud. 23, 175{196 (1985;Zbl 0581.68066)].
In the monograph under review, the present author presents in an integral form some of his mathematical results concerning knowledge spaces. There is an introductory chapter on Galois connections and their relational representations, one called \Structural minimization of quasi-orders", where a general notion of a basis is analysed in the context of partial orders, and one in which the introduced concepts are applied within the context of cognitive psychology: described is a specifc concept learning experiment in the domain of elementary algebra.
Mathematically most interesting is the final chapter on model-theoretic aspects of Galois connections, where a logical analysis is given for a class of Galois connections relating finitary relations to set systems and to the notion of logical entailment in propositional
logic. Janis Cirulis (Riga)
