{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,6]],"date-time":"2025-12-06T04:34:02Z","timestamp":1764995642906},"reference-count":5,"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":6401,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1996,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we study the logic of relational and partial variable sets, seen as a generalization of set-valued presheaves, allowing transition functions to be arbitrary relations or arbitrary partial functions. We find that such a logic is the usual intuitionistic and co-intuitionistic first order logic without Beck and Frobenius conditions relative to quantifiers along arbitrary terms. The important case of partial variable sets is axiomatizable by means of the substitutivity schema for equality. Furthermore, completeness, incompleteness and independence results are obtained for different kinds of Beck and Frobenius conditions.<\/jats:p>","DOI":"10.2307\/2275788","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:59:03Z","timestamp":1146956343000},"page":"843-872","source":"Crossref","is-referenced-by-count":7,"title":["Relational and partial variable sets and basic predicate logic"],"prefix":"10.1017","volume":"61","author":[{"given":"Silvio","family":"Ghilardi","sequence":"first","affiliation":[]},{"given":"Giancarlo","family":"Meloni","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200017151_ref005","first-page":"1","volume-title":"Applications of categorical algebra","volume":"XVII","author":"Lawvere","year":"1970"},{"key":"S0022481200017151_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0081355"},{"key":"S0022481200017151_ref001","unstructured":"Ghilardi S. and Meloni G. , Relative and absolute topological semantics for modal and basic predicate logic, in preparation."},{"key":"S0022481200017151_ref003","first-page":"59","volume-title":"Atti del congresso \u2018Nuovi problemi delta logica e delta filosofia delta scienza\u2019 Viareggio, Gennaio 1990, vol. II - Logica","author":"Ghilardi","year":"1991"},{"key":"S0022481200017151_ref004","first-page":"34","article-title":"Eine Interpretation des intuitionistischen Aussagenkalkiils","volume":"4","author":"G\u00f6del","year":"1933","journal-title":"Ergebnisse eines mathematischen Kolloquiums"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200017151","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T20:33:30Z","timestamp":1557693210000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200017151\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,9]]},"references-count":5,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,9]]}},"alternative-id":["S0022481200017151"],"URL":"https:\/\/doi.org\/10.2307\/2275788","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,9]]}}}