Topology via logic
Information systems for continuous posets
Theoretical Computer Science
Multi lingual sequent calculus and coherent spaces
Fundamenta Informaticae
Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
A Logic for Probabilities in Semantics
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Mathematical Structures in Computer Science
A universal characterization of the double powerlocale
Theoretical Computer Science - Logic, semantics and theory of programming
State-morphism algebras---General approach
Fuzzy Sets and Systems
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The category SCFrU of stably continuous frames and preframe homomorphisms (preserving finite meets and directed joins) is dual to the Karoubi envelope of a category Ent whose objects are sets and whose morphisms X → Y are upper closed relations between the finite powersets FX and FY. Composition of these morphisms is the "cut composition" of Jung et al. that interfaces disjunction in the codomains with conjunctions in the domains, and thereby relates to their multi-lingual sequent calculus. Thus stably locally compact locales are represented by "entailment systems" (X, ⊢) in which ⊢, a generalization of entailment relations, is idempotent for cut composition. Some constructions on stably locally compact locales are represented in terms of entailment systems: products, duality and powerlocales. Relational converse provides Ent with an involution, and this gives a simple treatment of the duality of stably locally compact locales. If A and B are stably continuous frames, then the internal preframe hom AψB is isomorphic to à ⊗ B where à is the Hofmann-Lawson dual. For a stably locally compact locale X, the lower powerlocale of X is shown to be the dual of the upper powerlocale of the dual of X.