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Bounded distributive lattices with strict implication

2005; Wiley; Volume: 51; Issue: 3 Linguagem: Inglês

10.1002/malq.200410022

1521-3870

Sergio A. Celani, Ramón Jansana,

Rough Sets and Fuzzy Logic

Mathematical Logic QuarterlyVolume 51, Issue 3 p. 219-246 Original Paper Bounded distributive lattices with strict implication Sergio Celani, Sergio Celani [email protected] Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto, 399, 7000 Tandil, ArgentinaSearch for more papers by this authorRamon Jansana, Corresponding Author Ramon Jansana [email protected] Departamento de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Baldiri i Reixach s/n, 08028 Barcelona, SpainPhone: +34 933 333 466, Fax: +34 934 498 510Search for more papers by this author Sergio Celani, Sergio Celani [email protected] Facultad de Ciencias Exactas, Universidad Nacional del Centro, Pinto, 399, 7000 Tandil, ArgentinaSearch for more papers by this authorRamon Jansana, Corresponding Author Ramon Jansana [email protected] Departamento de Lògica, Història i Filosofia de la Ciència, Universitat de Barcelona, Baldiri i Reixach s/n, 08028 Barcelona, SpainPhone: +34 933 333 466, Fax: +34 934 498 510Search for more papers by this author First published: 18 March 2005 https://doi.org/10.1002/malq.200410022Citations: 41AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract The present paper introduces and studies the variety WH of weakly Heyting algebras. It corresponds to the strict implication fragment of the normal modal logic K which is also known as the subintuitionistic local consequence of the class of all Kripke models. The tools developed in the paper can be applied to the study of the subvarieties of WH; among them are the varieties determined by the strict implication fragments of normal modal logics as well as varieties that do not arise in this way as the variety of Basic algebras or the variety of Heyting algebras. Apart from WH itself the paper studies the subvarieties of WH that naturally correspond to subintuitionistic logics, namely the variety of R-weakly Heyting algebras, the variety of T-weakly Heyting algebras and the varieties of Basic algebras and subresiduated lattices. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) References [1] M. 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