The Fixed-point Theorems of Priess-crampe and Ribenboim in Logic Programming

The Fixed - Point Theorems of

Sibylla Priess-Crampe and Paulo Ribenboim recently established a general xed-point theorem for multivalued mappings deened on generalized ultrametric spaces, and introduced it to the area of logic programming semantics. We discuss, in this context, the applications which have been made so far of this theorem and of its corollaries. In particular, we will relate these results to Scott-Ershov dom...

The Fixed - Point Theorems of Priess - Crampe and Ribenboim in Logi Programming

The Fixed-Point Theory of Strictly Contracting Functions on Generalized Ultrametric Semilattices

We introduce a new class of abstract structures, which we call generalized ultrametric semilattices, and in which the meet operation of the semilattice coexists with a generalized distance function in a tightly coordinated way. We prove a constructive fixed-point theorem for strictly contracting functions on directed-complete generalized ultrametric semilattices, and introduce a corresponding i...

Ultrametric Dynamics

This paper is concerned with dynamics in general ultrametric spaces. We prove the Fixed Point Theorem, the Stability Theorem, the Common Point Theorem, the Local Fixed Point Theorem, the Attractor Theorem and we derive conditions for a mapping to be surjective. We also discuss tightly continuous mappings and prove a theorem about the transfer of the property of principal completeness by a mappi...

A New Fixed - Point Theorem for Logic

We present a new xed-point theorem akin to the Banach contraction mapping theorem, but in the context of a novel notion of generalized metric space, and show how it can be applied to analyse the denotational semantics of certain logic programs. The theorem is obtained by generalizing a theorem of Priess-Crampe and Ribenboim, which grew out of applications within valuation theory, but is also in...