zbMATH — the first resource for mathematics

Formal models of reflexive structures. (English. Russian original) Zbl 1114.03313
Probl. Inf. Transm. 35, No. 1, 76-84 (1999); translation from Probl. Peredachi Inf. 35, No. 1, 90-99 (1999).
Formal models of reflection have been developed by V. A. Lefebvre in a number of papers and monographs since late 1960-ies. These models allow to describe states of a person and his reflections, in particular, the structure of iterated reflection like ”I think that he thinks that \(\ldots\)”. The paper under review begins with a short exposition of Lefebvre’s ideas. One of his models described in [V. A. Lefebvre: Structures and functions of natural reflection, in: Proc. Int. Conf., V. II System applications, N.Y., 359–363 (1984)]. is generalised, and related non-classical algebras of propositions are discussed in two further sections. Finally, improved is Lefebvre’s notion of a gamma-algebra from [V. A. Lefebvre, A Psychological Theory of Bipolarity and Reflexivity, Levinston, N.Y. (1992)]. The paper contains no mathematical results of any
03G25 Other algebras related to logic
68T30 Knowledge representation