Topological facets of the logic of subset spaces (with emphasis on canonical models)

Abstract

Among other things, this article makes a small contribution to the field of bi-topological modal logic, as it is examined herein to what extent Moss and Parikh's logic of subset spaces, LSS, is topologically relevant. For that purpose, several spatial characteristics are identified and proved to correspond with the axioms of this logic in the sense of topological definability first. It turns out that a certain bi-modal cover property plays a crucial part in doing so. Then, the question is raised whether these properties are valid on the canonical topo-model for LSS. Our investigation into this finally results in a topological characterization of that model, and it leads us to studying additional schemata in the same way, namely bi-modal commutation relations. As one of the questions opening our exposition asks for the nature of the topologies induced by the two LSS-modalities, we present a corresponding characterization in the concluding part of the article.