{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T14:08:26Z","timestamp":1778767706017,"version":"3.51.4"},"reference-count":40,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T00:00:00Z","timestamp":1643414400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100003030","name":"Ag\u00e8ncia de Gesti\u00f3 d'Ajuts Universitaris i de Recerca","doi-asserted-by":"publisher","award":["2017 SGR 95"],"award-info":[{"award-number":["2017 SGR 95"]}],"id":[{"id":"10.13039\/501100003030","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2022,2]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>For (finitary) deductive systems, we formulate a signature\u2010independent abstraction of the <jats:italic>weak excluded middle law<\/jats:italic> (WEML), which strengthens the existing general notion of an inconsistency lemma (IL). Of special interest is the case where a quasivariety  algebraizes a deductive system \u22a2. We prove that, in this case, if \u22a2 has a WEML (in the general sense) then every relatively subdirectly irreducible member of  has a greatest proper \u2010congruence; the converse holds if \u22a2 has an inconsistency lemma. The result extends, in a suitable form, to all protoalgebraic logics. A super\u2010intuitionistic logic possesses a WEML iff it extends . We characterize the IL and the WEML for normal modal logics and for relevance logics. A normal extension of  has a global consequence relation with a WEML iff it extends , while every axiomatic extension of  with an IL has a\u00a0WEML.<\/jats:p>","DOI":"10.1002\/malq.202100046","type":"journal-article","created":{"date-parts":[[2022,1,29]],"date-time":"2022-01-29T11:01:19Z","timestamp":1643454079000},"page":"79-94","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The algebraic significance of weak excluded middle laws"],"prefix":"10.1002","volume":"68","author":[{"given":"Tom\u00e1\u0161","family":"L\u00e1vi\u010dka","sequence":"first","affiliation":[{"name":"Institute of Information Theory and Automation of the Czech Academy of Sciences Pod Vod\u00e1renskou v\u011b\u017e\u00ed 4 182 00 Prague 8 Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tommaso","family":"Moraschini","sequence":"additional","affiliation":[{"name":"Department of Philosophy Faculty of Philosophy University of Barcelona Carrer de Montalegre 6 08001 Barcelona Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1071-2506","authenticated-orcid":false,"given":"James G.","family":"Raftery","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Applied Mathematics University of Pretoria Private Bag X20 Hatfield Pretoria 0028 Republic of South Africa"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2022,1,29]]},"reference":[{"key":"e_1_2_13_2_1","volume-title":"Entailment: The Logic of Relevance and Necessity","author":"Anderson A. 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