Abstract
Generalized metrics have been shown to be useful in many fields of Computer Science. In particular, partial metrics and quasi-metrics are used to develop quantitative mathematical models in denotational semantics and in asymptotic complexity analysis of algorithms, respectively. The aforesaid models are implemented independently and they are not related. However, it seems natural to consider a unique framework which remains valid for the applications to the both aforesaid fields. A first natural attempt to achieve that target suggests that the quantitative information should be obtained by means of the aggregation of a partial metric and a quasi-metric. Inspired by the preceding fact, we explore the way of merging, by means of a function, the aforementioned generalized metrics into a new one. We show that the induced generalized metric matches up with a partial quasi-metric. Thus, we characterize those functions that allow to generate partial quasi-metrics from the combination of a partial metric and a quasi-metric. Moreover, the relationship between the problem under consideration and the problems of merging partial metrics and quasi-metrics is discussed. Examples that illustrate the obtained results are also given.
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Acknowledgements
This research was partially supported by the Spanish Ministry of Economy and Competitiveness under Grant TIN2016-81731-REDT (LODISCO II) and AEI/FEDER, UE funds, by the Programa Operatiu FEDER 2014-2020 de les Illes Balears, by project ref. PROCOE/4/2017 (Direccio General d’Innovacio i Recerca, Govern de les Illes Balears), and by project ROBINS. The latter has received research funding from the EU H2020 framework under GA 779776. This publication reflects only the authors views and the European Union is not liable for any use that may be made of the information contained therein.
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Miñana, JJ., Valero, Ó. (2018). What Is the Aggregation of a Partial Metric and a Quasi-metric?. In: Medina, J., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Foundations. IPMU 2018. Communications in Computer and Information Science, vol 853. Springer, Cham. https://doi.org/10.1007/978-3-319-91473-2_20
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DOI: https://doi.org/10.1007/978-3-319-91473-2_20
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