Formal models of reflexive structures (Q1567732)

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