{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,24]],"date-time":"2025-09-24T10:20:51Z","timestamp":1758709251073,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Inspired by the seminal work of Hyland, Plotkin, and Power on the combination\nof algebraic computational effects via sum and tensor, we develop an analogous\ntheory for the combination of quantitative algebraic effects. Quantitative\nalgebraic effects are monadic computational effects on categories of metric\nspaces, which, moreover, have an algebraic presentation in the form of\nquantitative equational theories, a logical framework introduced by Mardare,\nPanangaden, and Plotkin that generalises equational logic to account for a\nconcept of approximate equality. As our main result, we show that the sum and\ntensor of two quantitative equational theories correspond to the categorical\nsum (i.e., coproduct) and tensor, respectively, of their effects qua monads. We\nfurther give a theory of quantitative effect transformers based on these two\noperations, essentially providing quantitative analogues to the following monad\ntransformers due to Moggi: exception, resumption, reader, and writer\ntransformers. Finally, as an application, we provide the first quantitative\nalgebraic axiomatizations to the following coalgebraic structures: Markov\nprocesses, labelled Markov processes, Mealy machines, and Markov decision\nprocesses, each endowed with their respective bisimilarity metrics. Apart from\nthe intrinsic interest in these axiomatizations, it is pleasing they have been\nobtained as the composition, via sum and tensor, of simpler quantitative\nequational theories.<\/jats:p>","DOI":"10.46298\/lmcs-20(4:9)2024","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T09:30:08Z","timestamp":1730194208000},"source":"Crossref","is-referenced-by-count":2,"title":["Sum and Tensor of Quantitative Effects"],"prefix":"10.46298","volume":"Volume 20, Issue 4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4004-6049","authenticated-orcid":false,"given":"Giorgio","family":"Bacci","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8660-1832","authenticated-orcid":false,"given":"Radu","family":"Mardare","sequence":"additional","affiliation":[]},{"given":"Prakash","family":"Panangaden","sequence":"additional","affiliation":[]},{"given":"Gordon","family":"Plotkin","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,10,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14636\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14636\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T09:30:08Z","timestamp":1730194208000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10761"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(4:9)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2212.11784v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2212.11784v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2212.11784","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2212.11784","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,10,29]]},"article-number":"10761"}}