{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:16Z","timestamp":1740123916586,"version":"3.37.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T00:00:00Z","timestamp":1713830400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T00:00:00Z","timestamp":1713830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Alma Mater Studiorum - Universit\u00e0 di Bologna"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Philos Logic"],"published-print":{"date-parts":[[2024,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a general approach to quantified modal logics that can simulate most other approaches. The language is based on operators indexed by terms which allow to express <jats:italic>de re<\/jats:italic> modalities and to control the interaction of modalities with the first-order machinery and with non-rigid designators. The semantics is based on a primitive counterpart relation holding between <jats:italic>n<\/jats:italic>-tuples of objects inhabiting possible worlds. This allows an object to be represented by one, many, or no object in an accessible world. Moreover by taking as primitive a relation between <jats:italic>n<\/jats:italic>-tuples we avoid some shortcoming of standard individual counterparts. Finally, we use cut-free labelled sequent calculi to give a proof-theoretic characterisation of the quantified extensions of each first-order definable propositional modal logic. In this way we show how to complete many axiomatically incomplete quantified modal logics.<\/jats:p>","DOI":"10.1007\/s10992-024-09754-7","type":"journal-article","created":{"date-parts":[[2024,4,23]],"date-time":"2024-04-23T08:02:01Z","timestamp":1713859321000},"page":"959-996","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quantified Modal Logics: One Approach to Rule (Almost) them All!"],"prefix":"10.1007","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4021-8667","authenticated-orcid":false,"given":"Eugenio","family":"Orlandelli","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,4,23]]},"reference":[{"key":"9754_CR1","doi-asserted-by":"publisher","first-page":"483","DOI":"10.5840\/monist200285434","volume":"85","author":"S Bauer","year":"2002","unstructured":"Bauer, S., & Wansing, H. (2002). Consequence, counterparts and substitution. The Monist, 85, 483\u2013497.","journal-title":"The Monist"},{"key":"9754_CR2","unstructured":"Belardinelli, F. (2007). Counterpart semantics for quantified modal logics. In The Logica Yearbook 2006. Filosofia, Prague"},{"key":"9754_CR3","doi-asserted-by":"crossref","unstructured":"Belardinelli, F. (2022). Counterpart semantics at work: Independence and incompleteness in quantified modal logics (p. 2022). Springer, Cham: In Thinking and calculating.","DOI":"10.1007\/978-3-030-97303-2_21"},{"key":"9754_CR4","unstructured":"van Benthem, J. (2010). Frame correspondences in modal predicate logic. In Proofs, Categories and Computations: Essays in Honor of Grigori Mints. College Publications, London."},{"key":"9754_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"P Blackburn","year":"2001","unstructured":"Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal Logic. Cambridge University Press."},{"key":"9754_CR6","volume-title":"First-order modal logic","author":"T Bra\u00fcner","year":"2006","unstructured":"Bra\u00fcner, T., & Ghilardi, S. (2006). First-order modal logic. Elsevier, New York: In Handbook of Modal Logic."},{"key":"9754_CR7","unstructured":"Corsi, G. (2009). Necessary for. In Logic, Methodology and Philosophy of Science, Proceedings of the$$13^{th}$$International Congress. King\u2019s College Publications, London"},{"key":"9754_CR8","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.1007\/s11225-013-9528-x","volume":"101","author":"G Corsi","year":"2013","unstructured":"Corsi, G., & Orlandelli, E. (2013). Free Quantified epistemic logics. Studia Logica, 101, 1159\u20131183.","journal-title":"Studia Logica"},{"key":"9754_CR9","unstructured":"Corsi, G., & Orlandelli, E. (2016). Sequent calculi for indexed epistemic logics. In: Proceedings of the 2nd International Workshop on Automated Reasoning in Quantified Non-Classical Logics (ARQNL 2016). CEUR-ws"},{"key":"9754_CR10","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/BF01048353","volume":"24","author":"M Cresswell","year":"1995","unstructured":"Cresswell, M. (1995). Incompleteness and the Barcan formula. Journal of Philosophical Logic, 24, 379\u2013403.","journal-title":"Journal of Philosophical Logic"},{"key":"9754_CR11","unstructured":"Cresswell, M. (2000). How to complete some modal predicate logics. In Advances in Modal Logic, vol. 2. CSLI Publications, Stanford"},{"key":"9754_CR12","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1017\/bsl.2015.7","volume":"21","author":"R Dyckhoff","year":"2015","unstructured":"Dyckhoff, R., & Negri, S. (2015). Geometrisation of first-order logic. Bulletin of Symbolic Logic, 21, 123\u2013163.","journal-title":"Bulletin of Symbolic Logic"},{"key":"9754_CR13","doi-asserted-by":"crossref","unstructured":"Fellin, G., Negri, S., & Orlandelli, E. (2023). Glivenko sequent classes and constructive cut elimination in geometric logics. Archive for Mathematical Logic, 62, 657\u2013688","DOI":"10.1007\/s00153-022-00857-z"},{"key":"9754_CR14","unstructured":"Fitting, M. (1991). Modal logic should say more than it does. In Computational Logic: Essays in Honor of Alan Robinson. MIT Press."},{"key":"9754_CR15","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.apal.2003.11.014","volume":"127","author":"M Fitting","year":"2004","unstructured":"Fitting, M. (2004). First-order intensional logic. Annals of Pure and Applied Logic, 127, 171\u2013193.","journal-title":"Annals of Pure and Applied Logic"},{"key":"9754_CR16","doi-asserted-by":"crossref","unstructured":"Fitting, M. (2020). De re, de dicto, and binding modalitities. In Knowledge, Proof and Dynamics: MIT Press.","DOI":"10.1007\/978-981-15-2221-5_8"},{"key":"9754_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-5292-1","volume-title":"First-Order Modal Logic","author":"M Fitting","year":"1998","unstructured":"Fitting, M., & Mendelsohn, R. L. (1998). First-Order Modal Logic. Springer."},{"key":"9754_CR18","unstructured":"Gabbay, D. M., Shehtman, V., & Skvortsov, D. (2009). Quantification in Nonclassical Logic, vol. 1. Elsevier"},{"key":"9754_CR19","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1007\/s10992-005-3664-3","volume":"34","author":"JW Garson","year":"2005","unstructured":"Garson, J. W. (2005). Unifying quantified modal logic. Journal of Philosophical Logic, 34, 621\u2013649.","journal-title":"Journal of Philosophical Logic"},{"key":"9754_CR20","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/BF00693273","volume":"4","author":"A Gibbard","year":"1975","unstructured":"Gibbard, A. (1975). Contingent identity. Journal of Philosophical Logic, 4, 187\u2013221.","journal-title":"Journal of Philosophical Logic"},{"key":"9754_CR21","doi-asserted-by":"publisher","first-page":"517","DOI":"10.2307\/2274697","volume":"56","author":"S Ghilardi","year":"1991","unstructured":"Ghilardi, S. (1991). Incompleteness results in Kripke semantics. Journal of Symbolic Logic, 56, 517\u2013538.","journal-title":"Journal of Symbolic Logic"},{"key":"9754_CR22","doi-asserted-by":"crossref","unstructured":"Ghilardi, S. (1992). Quantified extensions of canonical propositional intermediate logics. Studia Logica, 51, 195\u2013214.","DOI":"10.1007\/BF00370113"},{"key":"9754_CR23","doi-asserted-by":"crossref","unstructured":"Goldblatt, R. (2011). Quantifiers, Propositions and Identity. CUP, Cambridge.","DOI":"10.1017\/CBO9780511862359"},{"key":"9754_CR24","doi-asserted-by":"publisher","first-page":"319","DOI":"10.2307\/2025472","volume":"76","author":"AP Hazen","year":"1979","unstructured":"Hazen, A. P. (1979). Counterpart-theoretic semantics for modal logic. Journal of Philosophy, 76, 319\u2013338.","journal-title":"Journal of Philosophy"},{"key":"9754_CR25","doi-asserted-by":"publisher","DOI":"10.4324\/9780203290644","volume-title":"A New Introduction to Modal Logic","author":"GE Hughes","year":"1996","unstructured":"Hughes, G. E., & Cresswell, M. J. (1996). A New Introduction to Modal Logic. Routledge."},{"key":"9754_CR26","unstructured":"Kaplan, D. (1986). Opacity. Open Court, Chicago: In The Philosophy of W.V.O. Quine."},{"key":"9754_CR27","doi-asserted-by":"crossref","unstructured":"Kracht, M., & Kutz, O. (2002). The semantics of modal predicate logic. Part 1: completeness. In Advances in Modal Logic, vol.\u00a03. CSLI Publications, Stanford","DOI":"10.1142\/9789812776471_0016"},{"key":"9754_CR28","unstructured":"Kracht, M., & Kutz, O. (2005). The semantics of modal predicate logic. Part 2: modal individuals revisited. In Intensionality. A K Peters, Los Angeles"},{"key":"9754_CR29","unstructured":"Kupfer, M. (2014). Weak logic of modal metaframes. In The Logica Yearbook 2013. College Publications, London"},{"key":"9754_CR30","doi-asserted-by":"publisher","first-page":"113","DOI":"10.2307\/2024555","volume":"65","author":"D Lewis","year":"1968","unstructured":"Lewis, D. (1968). Counterpart theory for quantified modal logic. Journal of Philosophy, 65, 113\u2013126.","journal-title":"Journal of Philosophy"},{"key":"9754_CR31","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1305\/ndjfl\/1093870577","volume":"25","author":"F Montagna","year":"1984","unstructured":"Montagna, F. (1984). The predicate modal logic of provability. Notre Dame Journal of Formal Logic, 25, 179\u2013189.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"9754_CR32","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/s001530100124","volume":"42","author":"S Negri","year":"2003","unstructured":"Negri, S. (2003). Contraction-free sequent calculi for geometric theories with an application to Barr\u2019s theorem. Archive for Mathemathical Logic, 42, 389\u2013401.","journal-title":"Archive for Mathemathical Logic"},{"key":"9754_CR33","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s10992-005-2267-3","volume":"34","author":"S Negri","year":"2005","unstructured":"Negri, S. (2005). Proof analysis in modal logic. Journal of Philosophical Logic, 34, 507\u2013544.","journal-title":"Journal of Philosophical Logic"},{"key":"9754_CR34","unstructured":"Negri, S. (2009). Kriple completeness revisited. In Acts of knowledge: History, Philosophy, and Logic. College Publications, London."},{"key":"9754_CR35","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1093\/jigpal\/jzz015","volume":"27","author":"S Negri","year":"2019","unstructured":"Negri, S., & Orlandelli, E. (2019). Proof theory for quantified monotone modal logics. Logic Journal of the IGPL, 27, 478\u2013506.","journal-title":"Logic Journal of the IGPL"},{"key":"9754_CR36","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139003513","volume-title":"Proof Analysis","author":"S Negri","year":"2011","unstructured":"Negri, S., & von Plato, J. (2011). Proof Analysis. Cambridge: CUP."},{"key":"9754_CR37","doi-asserted-by":"publisher","first-page":"923","DOI":"10.1093\/logcom\/exab018","volume":"31","author":"E Orlandelli","year":"2021","unstructured":"Orlandelli, E. (2021). Labelled calculi for quantified modal logics with definite descriptions. Journal of Logic and Computation, 31, 923\u2013946.","journal-title":"Journal of Logic and Computation"},{"key":"9754_CR38","unstructured":"Rybakov, M, & Shkatov, D. (2018). A recursively enumerable Kripke complete first-order logic not complete with respect to a first-order definable class of frames. In Advances in Modal Logic, vol. 12. College Publications, London"},{"key":"9754_CR39","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/0168-0072(93)90210-5","volume":"63","author":"V Shehtman","year":"1993","unstructured":"Shehtman, V., & Skvortsov, D. (1993). Maximal Kripke-type semantics for modal and superintuitionistic predicate logics. Annals of Pure and Applied Logic, 63, 69\u2013101.","journal-title":"Annals of Pure and Applied Logic"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-024-09754-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10992-024-09754-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-024-09754-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T10:22:46Z","timestamp":1721298166000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10992-024-09754-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,23]]},"references-count":39,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,8]]}},"alternative-id":["9754"],"URL":"https:\/\/doi.org\/10.1007\/s10992-024-09754-7","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"type":"print","value":"0022-3611"},{"type":"electronic","value":"1573-0433"}],"subject":[],"published":{"date-parts":[[2024,4,23]]},"assertion":[{"value":"16 March 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}