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...

Rough set systems induced by equivalences have been proved to exhibit polymorphic logical behaviours in dependence on the extension of the set of completely defined objects. They give a rise to semi-simple Nelson algebras, hence three-valued Lukasiewicz algebras and regular double Stone algebras. Additionally, it has been shown that in the presence of completely defined objects, they fulfil a f...

. 1 Preliminaries Consider the variety Eω generated by the algebra ω := (N, ·), where i · j := max (i, j) for i 6= j, and i · j := 1 for i = j, i, j ∈ N1. These variety is a subvariety of the variety of equivalential algebras E . By an equivalential algebra we mean a grupoid A = (A,↔) that is a subreduct of a Brouwerian semilattice (or, equivalently, a Heyting algebra) with the operation ↔ give...

In this paper we describe the well-founded initial segment of the free Heyting algebra Aα on finitely many, α, generators. We give a complete classification of initial sublattices of A2 isomorphic to A1 (called ‘low ladders’), and prove that for 2 ≤ α < ω, the height of the wellfounded initial segment of Aα is ω.

Looking for a complete formalization of constructive topology we analyzed the structure of the subsets of a Heyting algebra which correspond to the concrete closed and open sets of a topological space over its formal points. After this has been done, the rules for a formalization of constructive topology, which is both predicative and complete, are unveiled.

We give a new order-theoretic characterization of a complete Heyting and co-Heyting algebra C. This result provides an unexpected relationship with the field of Nash equilibria, being based on the so-called Veinott ordering relation on subcomplete sublattices of C, which is crucially used in Topkis’ theorem for studying the order-theoretic stucture of Nash equilibria of supermodular games. Intr...

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...

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these d...