{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T15:47:00Z","timestamp":1781279220924,"version":"3.54.1"},"reference-count":28,"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":4940,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a sequent calculus<jats:bold>B<\/jats:bold>for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic. quantum and non-modal linear logics, are all obtained as extensions in a uniform way and in a single framework. We isolate three properties, which characterize<jats:bold>B<\/jats:bold>positively: reflection, symmetry and visibility.<\/jats:p><jats:p>A logical constant obeys to the principle of reflection if it is characterized semantically by an equation binding it with a metalinguistic link between assertions, and if its syntactic inference rules are obtained by solving that equation. All connectives of basic logic satisfy reflection.<\/jats:p><jats:p>To the control of weakening and contraction of linear logic, basic logic adds a strict control of contexts, by requiring that all active formulae in all rules are isolated, that is visible. From visibility, cut-elimination follows. The full, geometric symmetry of basic logic induces known symmetries of its extensions, and adds a symmetry among them, producing the structure of a cube.<\/jats:p>","DOI":"10.2307\/2586685","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:41Z","timestamp":1146938561000},"page":"979-1013","source":"Crossref","is-referenced-by-count":70,"title":["Basic logic: reflection, symmetry, visibility"],"prefix":"10.1017","volume":"65","author":[{"given":"Giovanni","family":"Sambin","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giulia","family":"Battilotti","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claudia","family":"Faggian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011762_ref018","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198538332.001.0001","volume-title":"Labelled deductive systems","volume":"1","author":"Gabbay","year":"1996"},{"key":"S0022481200011762_ref005","volume-title":"Logic in Florence '95, Proceedings of LMPS, Florence 1995","author":"Battilotti"},{"key":"S0022481200011762_ref028","volume-title":"Proof theory","author":"Takeuti","year":"1975"},{"key":"S0022481200011762_ref022","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(93)90093-S"},{"key":"S0022481200011762_ref002","unstructured":"Battilotti G. , An asymmetric sequent calculus for linear intuitionistic logic, submitted, 1998."},{"key":"S0022481200011762_ref021","volume-title":"Proof theory and logical complexity","author":"Girard","year":"1987"},{"key":"S0022481200011762_ref006","volume-title":"Preprint number 19","author":"Battilotti","year":"1993"},{"key":"S0022481200011762_ref004","volume-title":"Handbook of philosophical logic","volume":"VII","author":"Battilotti","year":"1998"},{"key":"S0022481200011762_ref019","first-page":"176\u2013210","article-title":"Untersuchungen \u00fcber das logische Schliessen","volume":"39","author":"Gentzen","year":"1935","journal-title":"Mathematische Zeitschrift"},{"key":"S0022481200011762_ref001","unstructured":"Battilotti G. , Logica di base attraverso il principio di reflessione, Ph.D. thesis , Universit\u00e0 di Siena, February 1997, advisor: G. 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