{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T12:39:59Z","timestamp":1783514399909,"version":"3.55.0"},"reference-count":4,"publisher":"Wiley","issue":"5","license":[{"start":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T00:00:00Z","timestamp":1159920000000},"content-version":"vor","delay-in-days":3,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2006,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The main purpose of this note is to characterize consistency of logic theories in propositional logic by means of topological concept. Based on the concepts of truth degree of formulas and similarity degree between formulas the concept of logic metric space has been proposed by the first author. It is proved in this note that a closed logic theory \u0393 is consistent if and only if it contains no interior point in the logic metric space. Moreover the relationship between logic closedness and topological closedness of a logic theory \u0393 is discussed. Finally, the concept of full divergency is also characterized by means of the topological concept of density. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200610007","type":"journal-article","created":{"date-parts":[[2006,10,4]],"date-time":"2006-10-04T14:30:49Z","timestamp":1159972249000},"page":"470-477","source":"Crossref","is-referenced-by-count":5,"title":["A topological characterization of consistency of logic theories in propositional logic"],"prefix":"10.1002","volume":"52","author":[{"given":"Guo\u2010Jun","family":"Wang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yan\u2010Hong","family":"She","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,10,4]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"A. G.Hamilton Logic for Mathematicians (Cambridge University Press 1978)."},{"key":"e_1_2_1_3_2","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1360\/02ys9122","article-title":"Theory of truth degrees of propositions in two\u2010valued logic","volume":"45","author":"Wang G.\u2010J.","year":"2002","journal-title":"Science in China, Ser. A"},{"key":"e_1_2_1_4_2","unstructured":"G.\u2010J.Wang Non\u2010Standard Mathematical Logic and Approximate Reasoning (in Chinese) (Science in China Press 2000)."},{"key":"e_1_2_1_5_2","unstructured":"G.\u2010J.Wang Introduction to Mathematical Logic and Resolution Principle (in Chinese) (Science in China Press 2003)."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200610007","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200610007","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T18:05:06Z","timestamp":1697652306000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200610007"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,10]]},"references-count":4,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2006,10]]}},"alternative-id":["10.1002\/malq.200610007"],"URL":"https:\/\/doi.org\/10.1002\/malq.200610007","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,10]]}}}