The daseinisation is a mapping from an orthomodular lattice in ordinary quantum theory into Heyting algebra topos theory. While distributivity does not always hold lattices, it algebras. We investigate the conditions under which negations and meets are preserved by daseinisation, condition that any element transformed through corresponds to original lattice. show these equivalent, that, only ca...

Let A be a Banach algebra and X a Banach A-bimodule, the derivation D : A → X is semi-inner if there are ξ, μ ∈ X such that D(a) = a.ξ − μ.a, (a ∈ A). A is called semi-amenable if every derivation D : A → X∗ is semi-inner. The dual Banach algebra A is Connes semi-amenable (resp. approximately semi-amenable) if, every D ∈ Z1w _ (A,X), for each normal, dual Banach A-bimodule X, is semi -inner (re...

This paper aims to contribute the extension of classical Formal Concept Analysis (FCA), allowing management unknown information. In a preliminary paper, we define new kind attribute implications represent knowledge from information currently available. The whole FCA framework has be appropriately extended manage introduces logic for reasoning with this implications, which belongs family logics ...

We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition. We show that our axiom ensures that a regular T1-space is separated and that regularity is preserved under initial constructions. Further we present an extension theorem for a c...

The lter construction, as an endo-functor on the category of small coherent categories, was used extensively by A. Pitts in a series of papers in the 80's to prove completeness and interpolation results. Later I. Moerdijk and E. Palmgren used the lter construction to construct non-standard models of Heyting arithmetic. In this paper we describe lter construction as a left-adjoint: applied to a ...

We study Nonassociative Lambek Calculus with additives ∧,∨, satisfying the distributive law (Distributive Full Nonassociative Lambek Calculus DFNL). We prove that categorial grammars based on DFNL, also enriched with assumptions, generate context-free languages. The proof uses proof-theoretic tools (interpolation) and a construction of a finite model, earlier employed in [11] in the proof of Fi...

Werner’s set-theoretical model is one of the most intuitive models of ECC. It combines a functional view of predicative universes with a collapsed view of the impredicative sort Prop. However this model of Prop is so coarse that the principle of excluded middle P ∨¬P holds. In this paper, we interpret Prop into a topological space (a special case of Heyting algebra) to make it more intuitionist...

This paper presents fuzzy graph rewriting systems with fuzzy relational calculus. In this paper fuzzy graph means crisp set of vetices and fuzzy set of edges. We provide $\mathrm{f}\mathrm{u}\mathrm{z},7,\mathrm{y}$ relational calculus witll Heyting algebra. Formalizing rewriting system of fuzzy graphs it is important to $\mathrm{c}\cdot 1_{1\mathrm{t})\mathrm{t}}.\mathrm{q}\mathrm{C}1$ how to ...

We prove that there exist profinite Heyting algebras are not isomorphic to the completion of any algebra. This resolves an open problem from 2009. More generally, we characterize those varieties in which completions. It turns out exists largest such. give different characterizations this variety and show it is finitely axiomatizable locally finite. From follows decidable whether a all members I...

According to a result by K. B. Lee, the lattice of varieties of pseudocomplemented distributive lattices is the ui + 1 chain B_i C Bo C Bi C • ■ ■ C Bn C •■ • C Bw in which the first three varieties are formed by trivial, Boolean, and Stone algebras respectively. In the present paper it is shown that any Stone algebra is determined within Bi by its endomorphism monoid, and that there are at mos...