In this paper we present a method for automated theorem proving in non-classical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestley-style representation for distributive lattices with operators in order to define a class of Kripke-style models with respect to which the logic is sound and complete. If this class of Krip...

We investigate Heyting varieties determined by prohibition of systems of configuraations in Priestley duals; we characterize the configuration systems yielding such varieties. On the other hand, the question whether a given finitely generated Heyting variety is obtainable by such means is solved for the special case of systems of trees. Priestley duality provides a correspondence between bounde...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

Duality theory emerged from the work by Marshall Stone [18] on Boolean algebras and distributive lattices in the 1930s. Later in the early 1970s Larisa Maksimova [10, 11] and Hilary Priestley [15, 16] developed analogous results for Heyting algebras, topological Boolean algebras, and distributive lattices. Duality for bounded, not necessarily distributive lattices, was developed by Alstir Urquh...

We provide new insights into the relationship between different constructions of the canonical extension of a bounded lattice. This follows on from the recent construction of the canonical extension using Ploščica’s maximal partial maps into the two-element set by Craig, Haviar and Priestley (2012). We show how this complete lattice of maps is isomorphic to the stable sets of Urquhart’s represe...

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.