{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T23:57:41Z","timestamp":1766102261851},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T00:00:00Z","timestamp":1488153600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2018,4]]},"abstract":"<jats:p>The study of algebraic modelling of labelled non-deterministic concurrent processes leads us to consider a category<jats:italic>L<jats:sub>B<\/jats:sub><\/jats:italic>, obtained from a complete meet-semilattice<jats:bold>B<\/jats:bold>and from<jats:bold>B<\/jats:bold>-valued equivalence relations. We prove that, if<jats:bold>B<\/jats:bold>has enough properties, then<jats:italic>L<jats:sub>B<\/jats:sub><\/jats:italic>presents a two-fold internal logical structure, induced by two doctrines definable on it: one related to its families of subobjects and one to its families of regular subobjects. The first doctrine is Heyting and makes<jats:italic>L<jats:sub>B<\/jats:sub><\/jats:italic>a Heyting category, the second one is Boolean. We will see that the difference between these two logical structures, namely the different behaviour of the negation operator, can be interpreted in terms of a distinction between non-deterministic and deterministic behaviours of agents able to perform computations in the context of the same process. Moreover, the sorted first-order logic naturally associated with<jats:italic>L<jats:sub>B<\/jats:sub><\/jats:italic>can be extended to a modal\/temporal logic, again using the doctrinal setting. Relations are also drawn to other computational models.<\/jats:p>","DOI":"10.1017\/s0960129517000019","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T01:42:07Z","timestamp":1488159727000},"page":"508-532","source":"Crossref","is-referenced-by-count":6,"title":["A doctrinal approach to modal\/temporal Heyting logic and non-determinism in processes"],"prefix":"10.1017","volume":"28","author":[{"given":"PAOLO","family":"BOTTONI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DANIELE","family":"GORLA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"STEFANO","family":"KASANGIAN","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANNA","family":"LABELLA","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,2,27]]},"reference":[{"key":"S0960129517000019_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S0960129509990272"},{"key":"S0960129517000019_ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jvlc.2011.11.006"},{"key":"S0960129517000019_ref2","unstructured":"Borceux F. (1994). Handbook of Categorical Algebra: Volume 1, Basic Category Theory, Encyclopedia of Mathematics and its Applications, Cambridge University Press. Available at http:\/\/opac.inria.fr\/record=b1126837"},{"key":"S0960129517000019_ref5","doi-asserted-by":"crossref","unstructured":"Cardelli L. (1982). Real time agents. In: Proceedings of the 9th Colloquium on Automata, Languages and Programming 94\u2013106. Available at http:\/\/dl.acm.org\/citation.cfm?id=646236.682864","DOI":"10.1007\/BFb0012760"},{"key":"S0960129517000019_ref12","doi-asserted-by":"crossref","unstructured":"Johnstone P. T. (2002). Sketches of An Elephant: A Topos Theory Compendium, vol. 1, Oxford Logic Guides, Clarendon Press. 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Enriched categories and presheaves: Their interconnections, generators and logics, Master's thesis, Universit\u00e0 degli studi di Milano."},{"key":"S0960129517000019_ref22","first-page":"283","article-title":"Sheaves and cauchy-complete categories","volume":"22","author":"Walters","year":"1981","journal-title":"Cahiers de Topologie et G\u00e9om\u00e9trie Diff\u00e9rentielle Cat\u00e9goriques"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129517000019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T18:13:29Z","timestamp":1719080009000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129517000019\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,27]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["S0960129517000019"],"URL":"https:\/\/doi.org\/10.1017\/s0960129517000019","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,27]]}}}