Logics of Filter Bubbles

Filter bubbles can be understood as configurations characterized by within-group proximity and separation from outsiders. Personalized feeds may form or preserve such configurations. We develop hybrid-style logics for reasoning about filter bubbles. The static logic characterizes bubble-shaped configurations, while its dynamic extension captures their formation and persistence under personalized feeds. We provide sound and strongly complete axiomatizations for the static and dynamic logics and prove their decidability.