Regular equivalence and dynamic logic

This paper describes a precise linguistic counterpart to the notion of a regular equivalence relation on a social network. That is, a formal language of position terms is defined with the property that on finite networks, two actors are regularly equivalent if and only if they cannot be distinguished by a position term. The paper also contains an exact characterization of the set of complex relations which are preserved under regular equivalences. The results presented here are known from logic and computer science, in which the mentioned language is called dynamic logic. The aim of the paper is to make these results available to social network analysts and explain why they are of interest to them. (C) 2002 Elsevier Science B.V. All rights reserved.