Based on a complete Heyting algebra, we modify the definition oflattice-valued fuzzifying convergence space using fuzzy inclusionorder and construct in this way a Cartesian-closed category, calledthe category of $L-$ordered fuzzifying convergence spaces, in whichthe category of $L-$fuzzifying topological spaces can be embedded.In addition, two new categories are introduced, which are called the...

The unit interval in a partially ordered abelian group with order unit forms an interval effect algebra (IEA) and can be regarded as an algebraic model for the semantics of a formal deductive logic. There is a categorical equivalence between the category of IEA’s and the category of unigroups. In this article, we study the IEA-unigroup connection, focusing on the cases in which the IEA is a Boo...

We introduce the concept of a connected logic (over S4) and show that each connected logic with the finite model property is the logic of a subalgebra of the closure algebra of all subsets of the real line R, thus generalizing theMcKinsey-Tarski theorem.As a consequence,weobtain that each intermediate logicwith thefinitemodel property is the logic of a subalgebra of the Heyting algebra of all o...

In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski showed that any Euclidean space Rn with n > 1 suffices, as does e.g. the Cantor space. In particular, intuitionistic logic cannot detect topological dimension in the frame of all open sets of a Euclidean spac...

We show that the model checking problem for intuitionistic propositional logic with one variable is complete for logspace-uniform AC. As basic tool we use the connection between intuitionistic logic and Heyting algebra, and investigate its complexity theoretical aspects. For superintuitionistic logics with one variable, we obtain NC-completeness for the model checking problem.

The main purpose of this paper is to axiomatize the join of the variety DPCSHC of dually pseudocomplemented semi-Heyting algebras generated by chains and the variety generated by D2, the De Morgan expansion of the four element Boolean Heyting algebra. Toward this end, we first introduce the variety DQDLNSH of dually quasi-De Morgan linear semi-Heyting algebras defined by the linearity axiom and...

The variety of Heyting algebras has two well-behaved locally finite reducts, the variety of bounded distributive lattices and the variety of implicative semilattices. The variety of bounded distributive lattices is generated by the→-free reducts of Heyting algebras while the variety of implicative semilattices by the ∨-free reducts. Each of these reducts gives rise to canonical formulas that ge...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the sam...