Non-deterministic Semantics for Dynamic Topological Logic

Dynamic Topological Logic ($\mathcal{DTL}$) is a combination of $\mathcal{S}${\em 4}, under its topological interpretation, and the temporal logic $\mathcal{LTL}$ interpreted over the natural numbers. $\mathcal{DTL}$ is used to reason about properties of dynamical systems based on topological spaces. Semantics are given by dynamic topological models, which are tuples $\left <X,\mathcal{T},f,V\right >$, where $\left <X,\mathcal{T}\right >$ is a topological space, $f$ a function on $X$ and $V$ a truth valuation assigning subsets of $X$ to propositional variables.