5 problems

Consider the trimodal $d$-logic of dynamical systems based on scattered spaces, where the trimodal language includes the henceforth operator and the tangled derivative. On scattere…

Let $\bold{DGL}$ be the extension of $\bold{GLC}$ that includes the temporal operator $*$. The tangled derivative operator is trivial on scattered spaces, so the original spatial o…

Let $\bold{GLC}$ be the dynamic logic of dynamical systems based on scattered spaces, and let $\mathcal{L}^{\circ*}_\lozenge$ be the trimodal topo-temporal language. Extend…

Let $\mathcal{DTL}^\ast$ be the dynamic topological logic with infinitary temporal modalities, and let $\mathsf L^\ast_{\Diamond f [f]\forall}$ be its monadic language with a unive…

The next-interior fragment uses the monadic modality $\Diamond$ and the next-time operator $f$. Over spaces with homeomorphisms, consider the proof system described in the cited wo…