{"id":168,"date":"2011-10-11T12:59:10","date_gmt":"2011-10-11T10:59:10","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=168"},"modified":"2014-01-11T22:22:36","modified_gmt":"2014-01-11T21:22:36","slug":"continuous-approximations-of-mv-algebras-with-product-and-product-residuation","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/168-continuous-approximations-of-mv-algebras-with-product-and-product-residuation\/","title":{"rendered":"Continuous approximations of MV-algebras with product and product residuation"},"content":{"rendered":"<p>Recently, MV-algebras with product have been investigated from different points of view. In particular a variety resulting from the combination of MV-algebras and product algebras \u00a0has been introduced. The elements of this variety are called L$\\Pi$-algebras. Even though the language of L$\\Pi$-algebras is strong enough to describe the main properties of product and of Lukasiewicz \u00a0connectives \u00a0on [0,1], the discontinuity of product implication introduces some problems in the applications, because a small error in the data may cause a relevant error in the output. In this paper we try to overcome this difficulty, substituting the product implication by a continuous approximation of it. The resulting algebras, the L$\\Pi_q$-algebras, are investigated in the present paper. In this paper we give a complete axiomatization of the quasivariety obtained in this way, and we show that such quasivariety is generated by the class of all L$\\Pi_q$-algebras whose lattice reduct is the unit interval [0,1] with the usual order.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dmi.unisa.it\/lucaspada\/wp-content\/uploads\/Articolo1.pdf\">Continuous approximations of MV-algebras with product and product residuation<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Recently, MV-algebras with product have been investigated from different points of view. In particular a variety resulting from the combination of MV-algebras and product algebras \u00a0has been introduced. The elements of this variety are called L$\\Pi$-algebras. Even though the language of L$\\Pi$-algebras is strong enough to describe the main properties of product and of Lukasiewicz [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[],"class_list":["post-168","post","type-post","status-publish","format-standard","hentry","category-preprint"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/168","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/comments?post=168"}],"version-history":[{"count":7,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/168\/revisions"}],"predecessor-version":[{"id":180,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/168\/revisions\/180"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=168"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=168"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=168"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}