Bisimulation and p-morphism for branching-time logics with indistinguishability relations

In Zanardo, 1998, the Peircean semantics for branching-time logics is enriched with a notion of indistinguishability at a moment t between histories passing through t. Trees with indistinguishability relations provide a semantics for a temporal language with tense and modal operators. In this paper a notion of p-morphism and a notion of bisimulation, wrt this language and semantics, are given and a number of preservation results are proven.