Dynamic Term-Modal Logic for Epistemic Social Network Dynamics (Extended Version)

Logics for social networks have been studied in recent literature. This paper presents a framework based on dynamic term-modal logic (DTML), a quantified variant of dynamic epistemic logic (DEL). In contrast with DEL where it is commonly known to whom agent names refer, 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 DTML semantics can represent a popular class of hybrid logic epistemic social network models. We also show that DTML can encode previously discussed dynamics for which finding a complete logic was left open. As complete reduction axioms systems exist for DTML, this yields a complete system for the dynamics in question.