Reasoning about epistemic social network dynamics using dynamic term-modal logic

Abstract

Abstract Logics for social networks have been studied in the recent literature. This paper presents a framework based on dynamic term-modal logic ($\textsf {DTML}$), a quantified variant of dynamic epistemic logic (DEL). In contrast with DEL where it is commonly known to whom agent names refer, $\textsf {DTML}$ can represent dynamics with uncertainty about agent identity. We exemplify dynamics where such uncertainty and de re/de dicto distinctions are key to social network epistemics. Technically, we show that $\textsf {DTML}$ semantics can represent a popular class of hybrid logic epistemic social network models. We also show that $\textsf {DTML}$ can encode previously discussed dynamics for which finding a complete logic was left open. As complete reduction axioms systems exist for $\textsf {DTML}$, this yields a complete system for the dynamics in question.