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...

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...

We develop a denotational, fully abstract semantics for constraint logic programming (clp) with respect to successful and failed observables. The denotational approach turns out very useful for the deenition of new operators on the language as the counterpart of some abstract operations on the denotational domain. In particular, by deening our domain as a cylindric Heyting algebra, we can explo...

This paper focuses on the equational class S„ of Brouwerian algebras and the equational class L„ of Heyting algebras generated by an »-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in Sn and L„ are characterized. Finally, free prod...

The lattice of z-ideals of the ring C(X) of real-valued continuous functions on a completely regular Hausdorff space X has been shown by Mart́ınez and Zenk to be a complete Heyting algebra with certain properties. We show that these properties are due only to the fact that C(X) is an f -ring with bounded inversion. This we do by studying lattices of algebraic z-ideals of abstract f -rings with b...

A bottom–up investigation of algebraic structures corresponding to many valued logical systems is made. Particular attention is given to the unit interval as a prototypical model of these kind of structures. At the top level of our construction, Heyting Wajsberg algebras are defined and studied. The peculiarity of this algebra is the presence of two implications as primitive operators. This cha...