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      Valuations revisited

      proceedings-article

      3rd Irish Workshop on Formal Methods (IWFM)

      Formal Methods

      1st - 2nd July 1999

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            Abstract

            The notion of a semivaluation has been introduced in [Sch98]. Aside from providing a novel concept generalizing valuations on lattices to the context of semilattices, semivaluations shed new light on the notion of a “partial metric” well known from theoretical computer science (e.g. [Mat94], [Mat95], [O’N97], [BS97] and [BSh97]). As discussed in [Sch98], the characterization of partial metrics in terms of semivaluations is non-trivial and involves the solution of an open problem of the Survey Paper “Non-symmetric Topology” (Problem 7 of [Kün93]) for the class of quasi-uniform semilattices. We recall from [Sch98] that the traditional domain theoretic examples, including the well known class of totally bounded Scott domains (e.g. [Smy91]), all correspond to semivaluation spaces. As such it is possible to study Quantitative Domain Theory (e.g. [FSW96]) in this simplified context, similar to the study of metric lattices (uniform lattices) in the more basic context of valuation spaces (cf. [Bir84] and also [Web91]). Hence the notion of a semivaluation is of sufficient interest to merit an independent study. The main purpose of this short note is to provide a basic introduction to the notion of a semivaluation independent of the domain theoretic considerations of [Sch98] and to discuss a recently obtained characterization of valuations in terms of semivaluations.

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            Author and article information

            Conference
            July 1999
            July 1999
            : 1-8
            Article
            10.14236/ewic/IWFM1999.15
            aa368776-e355-4fb2-ad11-aa7d4d5c8e0b
            © M. P. Schellekens. Published by BCS Learning and Development Ltd. 3rd Irish Workshop on Formal Methods

            This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

            3rd Irish Workshop on Formal Methods
            IWFM
            3
            Galway, Ireland
            1st - 2nd July 1999
            Electronic Workshops in Computing (eWiC)
            Formal Methods
            Product
            Product Information: 1477-9358BCS Learning & Development
            Self URI (journal page): https://ewic.bcs.org/
            Categories
            Electronic Workshops in Computing

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