Axiomatizing Hybrid Products of Monotone Neighborhood Frames

The main aim of this paper is to propose a robust way to combine two monotone hybrid logics. This work can be regarded as a further extension of both topological semantics for hybrid logic (Ten Cate and Litak 2007) and bi-hybrid logic of products of Kripke frames (Sano 2010). First, we generalize the notion of product of topologies (Van Benthem, et al 2006) to the monotone neighborhood frames and introduce two kinds of nominals: i (e.g. for a moment of time) and a (e.g. for a spatial point), and the corresponding satisfaction operators: @i and @a to describe a product of monotone neighborhood frames. Second, we give five interaction axioms and establish a general completeness result called pure completeness of bi-hybrid logic of monotone neighborhood frames. By extending this, we also establish a pure completeness result of bi-hybrid logic of products of topologies.