Abstract

In several semantics for branching-time logic, the evaluation rules involve a quantification over the set of all histories in a given tree-like structure T. These semantics are often generalized by replacing these quantifications by quantifications over a bundle in T, that is, over a set of histories fulfilling suitable closure properties. According to this generalization, the basic semantical structures are pairs 〈T, B〉 in which B is a bundle in T.The problem of the definability of the class of complete bundled trees, in a given class G, concerns the existence of a set Γ of formulas such that, for every bundled tree 〈T, B〉 in G, Γ is true in 〈T, B〉 if and only if B is the set of all histories in T. In Ockhamist branching-time logic, sets Γ corresponding to particular classes G have been found. It will be proved that Γ does not exist if G is the class of all bundled trees