The powerset monad on the category of sets does not distribute over itself. Nevertheless a
weaker form of distributive law of the powerset monad over itself exists and it essentially …

We study the poset NO (B) of necessity operators on a boolean algebra B. We show that NO
(B) is a meet-semilattice that need not be distributive. However, when B is complete, NO (B) …

Stone duality generalizes to an equivalence between the categories Stone R of Stone
spaces and closed relations and BA S of boolean algebras and subordination relations …

We generalize the classic Vietoris endofunctor to the category of compact Hausdorff spaces
and closed relations. The lift of a closed relation is done by generalizing the construction of …

$\mathsf {S5} $-subordination algebras are a natural generalization of de Vries algebras.
Recently it was proved that the category $\mathsf {SubS5^ S} $ of $\mathsf {S5} …

Monads are a concept from category theory allowing to model abstractly the notion of
computational effect. The non-compositionality of monads is well-known, but the theory of …

S5-subordination algebras were recently introduced as a generalization of de Vries
algebras, and it was proved that the category SubS5S of S5-subordination algebras and …

The symmetric strict implication calculus is a modal calculus for compact Hausdorff spaces.
This is established through de Vries duality, linking compact Hausdorff spaces with de Vries …

Let $\pi: Y\rightarrow X $ be a continuous surjection between compact Hausdorff spaces $ Y
$ and $ X $ which is irreducible in the sense that if $ F\subsetneq Y $ is closed, then $\pi …

There is a recent interest in probabilistic programming amongst the theoretical computer
science community [144, 74, 73, 133, 48, 40, 49], fitting within a long-established tradition of …