A probabilistic powerdomain of evaluations
Proceedings of the Fourth Annual Symposium on Logic in computer science
Semantics of programming languages: structures and techniques
Semantics of programming languages: structures and techniques
Totally bounded spaces and compact ordered spaces as domains of computation
Topology and category theory in computer science
Probabilistic non-determinism
An extensional treatment of lazy data flow deadlock
Selected papers of the workshop on Topology and completion in semantics
Generalized metric spaces: completion, topology, and power domains via the Yoneda embedding
Theoretical Computer Science
Partial Metrics and Co-continuous Valuations
FoSSaCS '98 Proceedings of the First International Conference on Foundations of Software Science and Computation Structure
Towards Computing Distances Between Programs via Scott Domains
LFCS '97 Proceedings of the 4th International Symposium on Logical Foundations of Computer Science
Quasi Uniformities: Reconciling Domains with Metric Spaces
Proceedings of the 3rd Workshop on Mathematical Foundations of Programming Language Semantics
Semantics of Exact Real Arithmetic
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Fundamenta Informaticae
A characterization of partial metrizability: domains are quantifiable
Theoretical Computer Science - Topology in computer science
Theoretical Computer Science - Spatial representation: Discrete vs. continous computational models
Denotational semantics for programming languages, balanced quasi-metrics and fixed points
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
On the structure of the space of complexity partial functions
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
A quantitative computational model for complete partial metric spaces via formal balls†
Mathematical Structures in Computer Science
The Hausdorff fuzzy quasi-metric
Fuzzy Sets and Systems
Domain theoretic characterisations of quasi-metric completeness in terms of formal balls†
Mathematical Structures in Computer Science
Coupled fixed point results for (ψ,φ)-weakly contractive condition in ordered partial metric spaces
Computers & Mathematics with Applications
A generalized contraction principle with control functions on partial metric spaces
Computers & Mathematics with Applications
Hyperspaces of a weightable quasi-metric space: Application to models in the theory of computation
Mathematical and Computer Modelling: An International Journal
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Partial metrics, or the equivalent weightable quasi-metrics, have been introduced in Matthews (Proc. 8th Summer Conf. on General Topology and Applications; Ann. New York Acad. Sci. 728 (1994) 183) as part of the study of the denotational semantics of data flow networks (Theoret. Comput. Sci. 151 (1995) 195). The interest in valuations in connection to Domain Theory derives from e.g. Jones and Plotkin (LICS '89, IEEE Computer Society Press, Silver Spring, MD, 1998, pp. 186-195), Jones (Ph.D. Thesis, University of Edinburgh, 1989), Edalat (LICS'94, IEEE Computer Society Press, Silver Spring, MD, 1994) and Heckmann (Fund. Inform. 24(3) (1995) 259). Connections between partial metrics and valuations have been discussed in the literature, e.g. O'Neill (in: S. Andima et al. (Eds.), Proc. 11th Summer Conf. on General Topology and Applications; Ann. New York Acad. Sci. 806 (1997) 304), Bukatin and Scott (in: S. Adian, A. Nerode (Eds.), Logical Foundations of Computer Science, Lecture Notes in Computer Science, Vol. 1234, Springer, Berlin, 1997, pp. 33-43) and Bukatin and Shorina (in: M. Nivat (Ed.), Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science, Vol. 1378, Springer, Berlin, 1998, pp. 125-139). In each case, partial metrics are generated from strictly increasing valuations.We analyze the precise relationship between these two notions. It is well known that characterizations of partial metrics in general are hard to obtain, as witnessed by the open characterization problems in the survey paper Nonsymmetric Topology (Kúnzi (Bolyai Soc. Math. Stud. 4 (1993) 303). Our approach to obtaining such a characterization involves the isolation of a "mathematically nice" class of spaces, which is sufficiently large to incorporate the quantitative domain theoretic examples involving partial metric spaces.For these purposes we focus on the class of quasi-metric semilattices. These structures, as will be illustrated, arise naturally in quantitative domain theory and include in particular the class of totally bounded Scott domains discussed in Smyth (in: G.M. Reed, A.W. Roscoe, R.F. Wachter (Ed.), Topology and Category Theory in Computer Science, Oxford University Press, Oxford, 1991, pp. 207-229), the Baire quasi-metric spaces of (Theoret. Comput. Sci. 151 (1995) 195), the complexity spaces of Schellekens (in: Proc. MFPS 11, Electronic Notes in Theoretical Computer Science, Vol. I, Elsevier, Amsterdam, 1995, pp. 211-232) and the interval domain (Proc. Twelfth Ann. IEEE Symp. on Logic in Computer Science, IEEE Press, New York, 1997, pp. 248-257).We introduce the notion of a semivaluation, which generalizes the fruitful notion of a valuation on a lattice to the context of semilattices and establish a correspondence between partial metric semilattices and semivaluation spaces.