Intuitionistic logic with a Galois connection has the finite model property

We show that the intuitionistic propositional logic with a Galois connection (IntGC), introduced by the authors, has the finite model property.Comment: 6 page

Difference functions of dependence spaces

Here the reduction problem is studied in an algebraic structure called dependence space. We characterize the reducts by the means of dense families of dependence spaces. Dependence spaces defined by indiscernibility relations are also considered. We show how we can determine dense families of dependence spaces induced by indiscernibility relations by applying indiscernibility matrices. We also study difference functions which connect the reduction problem to the general problem of identifying the set of all minimal Boolean vectors satisfying an isotone Boolean function

Pseudo-Kleene algebras determined by rough sets

We study the pseudo-Kleene algebras of the Dedekind-MacNeille completion of the ordered set of rough set determined by a reflexive relation. We characterize the cases when PBZ and PBZ*-lattices can be defined on these pseudo-Kleene algebras.Comment: 24 pages, minor update to the initial versio

Defining rough sets as core-support pairs of three-valued functions

We answer the question what properties a collection $\mathcal{F}$ of three-valued functions on a set $U$ must fulfill so that there exists a quasiorder $\leq$ on $U$ such that the rough sets determined by $\leq$ coincide with the core--support pairs of the functions in $\mathcal{F}$. Applying this characterization, we give a new representation of rough sets determined by equivalences in terms of three-valued {\L}ukasiewicz algebras of three-valued functions.Comment: This version is accepted for publication in Approximate Reasoning (May 2021