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

TL;DR

This paper introduces a dynamic term-modal logic framework for modeling social network epistemics, capable of representing uncertainty about agent identities and complex social dynamics, with completeness results for the logic.

Contribution

It develops a novel dynamic term-modal logic that handles agent identity uncertainty and extends hybrid logic models for social network epistemics.

Findings

DTML can represent social network dynamics with uncertain agent identities.

The framework encodes complex social epistemic scenarios previously unresolved.

A complete axiomatization for the proposed dynamics is established.

Abstract

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.