{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T13:14:08Z","timestamp":1778764448014,"version":"3.51.4"},"reference-count":26,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T00:00:00Z","timestamp":1744070400000},"content-version":"unspecified","delay-in-days":97,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2025]]},"abstract":"<jats:title>Abstract<\/jats:title>\n\t  <jats:p>We present an axiom system for what we call Prior\u2019s Ideal Language and prove its completeness and pure completeness with respect to general models. With this is done, we explain, with examples, why this system provides a useful setting for exploring Arthur Prior\u2019s work.<\/jats:p>","DOI":"10.1017\/s0960129525000076","type":"journal-article","created":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T06:14:40Z","timestamp":1744092880000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Prior\u2019s ideal language"],"prefix":"10.1017","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9345-552X","authenticated-orcid":false,"given":"Patrick","family":"Blackburn","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4582-1702","authenticated-orcid":false,"given":"Torben","family":"Bra\u00fcner","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Julie Lundbak","family":"Kofod","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,4,8]]},"reference":[{"key":"S0960129525000076_ref7","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1007\/s11229-005-5512-y","article-title":"Arthur prior and hybrid logic","volume":"150","author":"Blackburn","year":"2006","journal-title":"Synthese"},{"key":"S0960129525000076_ref20","volume-title":"Papers on Time and Tense","author":"Prior","year":"1968"},{"key":"S0960129525000076_ref21","volume-title":"Papers on Time and Tense","author":"Prior","year":"2003"},{"key":"S0960129525000076_ref3","unstructured":"Areces, C. E. (2000). Logic Engineering: The Case of Description and Hybrid Logics. Phd thesis, Institute for Logic, Language and Computation."},{"key":"S0960129525000076_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2018.07.004"},{"key":"S0960129525000076_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-006-9009-6"},{"key":"S0960129525000076_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2023.33"},{"key":"S0960129525000076_ref24","volume-title":"Worlds, Times, and Selves","author":"Prior","year":"1977"},{"key":"S0960129525000076_ref23","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1305\/ndjfl\/1093956750","article-title":"On a family of paradoxes","volume":"2","author":"Prior","year":"1961","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0960129525000076_ref1","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/s10992-012-9260-4","article-title":"Completeness in hybrid type theory","volume":"43","author":"Areces","year":"2014","journal-title":"Journal of Philosophical Logic"},{"key":"S0960129525000076_ref4","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/S1570-2464(07)80017-6","volume-title":"Handbook of Modal Logic","author":"Areces","year":"2007"},{"key":"S0960129525000076_ref10","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/BF01049415","article-title":"Hybrid languages","volume":"4","author":"Blackburn","year":"1995","journal-title":"Journal of Logic, Language and Information"},{"key":"S0960129525000076_ref14","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Copeland","year":"2017"},{"key":"S0960129525000076_ref5","volume-title":"the Description Logic Handbook: Theory, Implementation and Applications","author":"Baader","year":"2003"},{"key":"S0960129525000076_ref25","doi-asserted-by":"crossref","unstructured":"Ten Cate, B. (2005). Model Theory for Extended Modal Languages. Phd thesis, Institute for Logic, Language and Computation.","DOI":"10.2178\/jsl\/1107298517"},{"key":"S0960129525000076_ref8","doi-asserted-by":"crossref","unstructured":"Blackburn, P. , Bra\u00fcner, T. and Kofod, J. (2023). An axiom system for basic hybrid logic with propositional quantifiers. In: Logic, Language, Information, and Computation \u2013 29th International Workshop, WoLLIC. 2023, Proceedings, Lecture Notes in Computer Science, vol. 13923, Springer-Verlag, 118\u2013134.","DOI":"10.1007\/978-3-031-39784-4_8"},{"key":"S0960129525000076_ref2","doi-asserted-by":"publisher","DOI":"10.2307\/2695090"},{"key":"S0960129525000076_ref12","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Bra\u00fcner","year":"2021"},{"key":"S0960129525000076_ref16","doi-asserted-by":"crossref","first-page":"81","DOI":"10.2307\/2266967","article-title":"Completeness in the theory of types","volume":"15","author":"Henkin","year":"1950","journal-title":"The Journal of Symbolic Logic"},{"key":"S0960129525000076_ref17","unstructured":"Kofod, J. L. (2022). What on Earth was Arthur Prior Thinking?: About Physics and Hybrid Logic. Phd thesis, IKH, Roskilde University."},{"key":"S0960129525000076_ref26","doi-asserted-by":"crossref","first-page":"150","DOI":"10.2307\/2272558","article-title":"Semantic analysis of tense logics","volume":"37","author":"Thomason","year":"1972","journal-title":"The Journal of Symbolic Logic"},{"key":"S0960129525000076_ref19","volume-title":"Temporal Logic: From Ancient Ideas to Artificial Intelligence","volume":"57","author":"\u00d8hrstr\u00f8m","year":"2007"},{"key":"S0960129525000076_ref15","doi-asserted-by":"crossref","first-page":"336","DOI":"10.1111\/j.1755-2567.1970.tb00432.x","article-title":"Propositional quantifiers in modal logic","volume":"36","author":"Fine","year":"1970","journal-title":"Theoria"},{"key":"S0960129525000076_ref13","doi-asserted-by":"publisher","DOI":"10.2307\/2271102"},{"key":"S0960129525000076_ref22","doi-asserted-by":"crossref","first-page":"261","DOI":"10.2307\/2964285","article-title":"Epimenides the Cretan","volume":"23","author":"Prior","year":"1958","journal-title":"The Journal of Symbolic Logic"},{"key":"S0960129525000076_ref9","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"Blackburn","year":"2001"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129525000076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,8]],"date-time":"2025-04-08T06:15:32Z","timestamp":1744092932000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129525000076\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":26,"alternative-id":["S0960129525000076"],"URL":"https:\/\/doi.org\/10.1017\/s0960129525000076","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}],"article-number":"e7"}}