Regular Equivalence and Dynamic Logic
Maarten Marx, Michael Masuch
Abstract:
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.
Keywords: social networks, regular equivalence, position analysis,
bisimulation, dynamic logic, modal logic, description logic