{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:40:38Z","timestamp":1707032438858},"reference-count":15,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11150,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1983,9]]},"abstract":"<jats:p>In spite of the philosophical significance of higher-order modal logic, the modal logician's main concern has been with sentential logic. In this paper we do not intend to go into philosophical details, but we only remark that higher-order modal logic has a close relationship with Montague's well-known idea of \u201cuniversal grammar\u201d, which is an ambitious attempt to build a logical theory of natural languages with exact syntax and semantics, comparable with the artificial languages of mathematical logic. For this matter, the reader can consult, e.g., Montague [8], [9] and Gallin [2].<\/jats:p>","DOI":"10.2307\/2273466","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:04:45Z","timestamp":1146953085000},"page":"744-751","source":"Crossref","is-referenced-by-count":0,"title":["Hauptsatz for higher-order modal logic"],"prefix":"10.1017","volume":"48","author":[{"given":"Hirokazu","family":"Nishimura","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200037919_ref013","doi-asserted-by":"publisher","DOI":"10.2969\/jmsj\/01940399"},{"key":"S0022481200037919_ref009","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1111\/j.1755-2567.1970.tb00434.x","article-title":"Universal grammar","volume":"36","author":"Kripke","year":"1970","journal-title":"Theoria"},{"key":"S0022481200037919_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF00413599"},{"key":"S0022481200037919_ref006","first-page":"1","volume":"24","author":"Kripke","year":"1959","journal-title":"A completeness theorem in modal logic"},{"key":"S0022481200037919_ref005","volume-title":"Provability in logic","author":"Kanger","year":"1957"},{"key":"S0022481200037919_ref004","first-page":"159","volume":"14","author":"Henkin","year":"1949","journal-title":"Completeness in the theory of types"},{"key":"S0022481200037919_ref002","volume-title":"Intensional and higher order modal logic","author":"Gallin","year":"1975"},{"key":"S0022481200037919_ref001","volume-title":"Modal logics","author":"Feys","year":"1965"},{"key":"S0022481200037919_ref011","first-page":"452","volume":"33","author":"Prawitz","year":"1968","journal-title":"Hauptsatz for higher order logic"},{"key":"S0022481200037919_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19630090502"},{"key":"S0022481200037919_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201363"},{"key":"S0022481200037919_ref010","first-page":"113","article-title":"Gentzen method in modal calculi","volume":"9","author":"Ohnishi","year":"1957","journal-title":"Osaka Mathematical Journal"},{"key":"S0022481200037919_ref015","volume-title":"Proof theory","author":"Takeuti","year":"1975"},{"key":"S0022481200037919_ref012","first-page":"305","volume":"25","author":"Sch\u00fctte","year":"1960","journal-title":"Syntactical and semantical properties of simple type theory"},{"key":"S0022481200037919_ref014","first-page":"127","article-title":"A system of simple type theory of Gentzen style with inference on extensionality, and the cut-elimination in it","volume":"18","author":"Takahashi","year":"1970","journal-title":"Commentarii Mathematici Universitatis Sancti Pauli"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200037919","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:24:32Z","timestamp":1707031472000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200037919\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1983,9]]}},"alternative-id":["S0022481200037919"],"URL":"https:\/\/doi.org\/10.2307\/2273466","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,9]]}}}