{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T15:40:04Z","timestamp":1774453204688,"version":"3.50.1"},"reference-count":9,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present an axiomatization for Basic Propositional Calculus BPC and give a completeness theorem for the class of transitive Kripke structures. We present several refinements, including a completeness theorem for irreflexive trees. The class of intermediate logics includes two maximal nodes, one being Classical Propositional Calculus CPC, the other being <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub>, a theory axiomatized by T \u2192 \u22a5. The intersection CPC \u2229 <jats:italic>E<\/jats:italic><jats:sub>1<\/jats:sub> is axiomatizable by the Principle of the Excluded Middle <jats:italic>A<\/jats:italic> V \u2228 \u231d<jats:italic>A<\/jats:italic>. If <jats:italic>B<\/jats:italic> is a formula such that (T \u2192 <jats:italic>B<\/jats:italic>) \u2192 <jats:italic>B<\/jats:italic> is not derivable, then the lattice of formulas built from one propositional variable <jats:italic>p<\/jats:italic> using only the binary connectives, is isomorphically preserved if <jats:italic>B<\/jats:italic> is substituted for <jats:italic>p<\/jats:italic>. A formula (T \u2192 <jats:italic>B<\/jats:italic>) \u2192 <jats:italic>B<\/jats:italic> is derivable exactly when <jats:italic>B<\/jats:italic> is provably equivalent to a formula of the form ((T \u2192 <jats:italic>A<\/jats:italic>) \u2192 <jats:italic>A<\/jats:italic>) \u2192 (T \u2192 <jats:italic>A<\/jats:italic>).<\/jats:p>","DOI":"10.1002\/malq.19980440304","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T23:23:45Z","timestamp":1180567425000},"page":"317-343","source":"Crossref","is-referenced-by-count":58,"title":["Basic Propositional Calculus I"],"prefix":"10.1002","volume":"44","author":[{"given":"Mohammad","family":"Ardeshir","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wim","family":"Ruitenburg","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"Ardeshir M. Aspects of Basic Logic. PhD Thesis Department of Mathematics Statistics and Computer Science Marquette University Milwaukee1995."},{"key":"e_1_2_1_3_2","volume-title":"The Unprovability of Consistency: An Essay in Modal Logic","author":"Boolos G.","year":"1979"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2964568"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093894226"},{"key":"e_1_2_1_6_2","first-page":"271","article-title":"Constructive logic and the paradoxes","volume":"1","author":"Ruitenburg W.","year":"1991","journal-title":"Modern Logic"},{"key":"e_1_2_1_7_2","first-page":"121","volume-title":"Dirk van Dalen Festschrift, Quaestiones Infinitae","author":"Ruitenburg W.","year":"1993"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1755-2567.1970.tb00429.x"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8601-8"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01874706"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440304","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440304","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:50:08Z","timestamp":1698540608000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440304"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440304"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440304","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}