Topological semantics for paraconsistent and paracomplete logics in Isabelle/HOL

We encode a topological semantics for paraconsistent and paracomplete logics enriched with recovery operators, by drawing upon early works on topological Boolean algebras (by Kuratowski, Zarycki, McKinsey & Tarski, etc.). This work exemplarily illustrates the shallow semantical embedding approach using Isabelle/HOL and shows how we can effectively harness theorem provers, model finders and "hammers" for reasoning with quantified non-classical logics.