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      Valuations revisited

      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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          Most cited references 5

          • Record: found
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          Partial Metric Topology

           S Matthews (1994)
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            • Record: found
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            • Article: not found

            An extensional treatment of lazy data flow deadlock

             S.G. Matthews (1995)
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              • Record: found
              • Abstract: not found
              • Article: not found

              Lengths on semigroups and groups

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                Author and article information

                Conference
                July 1999
                July 1999
                : 1-8
                Article
                10.14236/ewic/IWFM1999.15
                © 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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