Hu's characterization of metric completeness revisited

Completeness in Probabilistic Metric Spaces

The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...

A Kirk Type Characterization of Completeness for Partial Metric Spaces

Modularity of Completeness Revisited

One of the key results in the eld of modularity for Term Rewriting Systems is the modularity of completeness for left linear TRSs established by Toyama Klop and Barendregt in TKB The proof however is quite long and involved In this paper a new proof of this basic result is given which is both short and easy employing the powerful technique of pile and delete already used with success in proving...

Kripke completeness revisited

The evolution of completeness proofs for modal logic with respect to the possible world semantics is studied starting from an analysis of Kripke’s original proofs from 1959 and 1963. The critical reviews by Bayart and Kaplan and the emergence of Henkin-style completeness proofs are detailed. It is shown how the use of a labelled sequent system permits a direct and uniform completeness proof for...

Denotational Completeness Revisited

We deene a notion of Kripke logical predicate for models of classical linear logic. A Kripke logical predicate on a type A will be a set of generalised elements of A satisfying certain closure properties. Denotations of proofs of A will be characterised as those global elements of A satisfying all Kripke logical predicates on A.