Topological aspects of branching-time semantics
This paper presents a new perspective under which branching-time semantics can be viewed. Branching-time is usually represented by a tree; a history is to be considered here as a maximal linearly ordered set in the tree-like representation of time. The main aim of the paper is to investigate the structure of the set of histories in a tree from a topological perspective. The set of histories in a tree structure can be endowed in a natural way with a topological structure which generates a non-archimedean topological space. In this way it is possible to consider the new notion of topological validity of temporal formulae under the Ockhamist semantics, i.e. formulas are true or false at pairs \((t,h)\) where \(t\) is an instant and \(h\) is a history. It is proved that this notion of validity is equivalent to validity with respect to bundled trees, that is, under the assumption that the possibility operators do not quantify over the set of all histories, but on a fixed subset (bundle) fulfilling a suitable closure property.
scientific article; zbMATH DE number 2027180