{"id":191,"date":"2011-10-11T13:19:48","date_gmt":"2011-10-11T11:19:48","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=191"},"modified":"2017-10-05T09:51:24","modified_gmt":"2017-10-05T08:51:24","slug":"lpi-logic-with-fixed-points","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/191-lpi-logic-with-fixed-points\/","title":{"rendered":"LPi Logic with Fixed Points"},"content":{"rendered":"<p>We study a system, $\\mu$L$\\Pi$, obtained by an expansion of \u00a0L$\\Pi$ logic with fixed points connectives. The first main result of the paper is that $\\mu$L$\\Pi$ is standard complete, i.e. complete with regard to the unit interval of real numbers endowed with a suitable structure.<br \/>\nWe also prove that the class of algebras which forms algebraic semantics for this logic is generated, as a variety, by its linearly ordered members and that they are precisely the interval algebras of real closed fields. This correspondence is extended to a categorical equivalence between the whole category of those algebras and another category naturally arising from real closed fields.<br \/>\nFinally, we show that this logic enjoys implicative interpolation.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/Fix-inviato.pdf\">LPi Logic with Fixed Points<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study a system, $\\mu$L$\\Pi$, obtained by an expansion of \u00a0L$\\Pi$ logic with fixed points connectives. The first main result of the paper is that $\\mu$L$\\Pi$ is standard complete, i.e. complete with regard to the unit interval of real numbers endowed with a suitable structure. We also prove that the class of algebras which forms [&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":[74,73,28,75,77,66,76],"class_list":["post-191","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-fixed-point","tag-llogic","tag-lukasiewicz-logic","tag-many-valued-logic","tag-product-logic","tag-real-closed-field","tag-standard-completeness"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/191","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=191"}],"version-history":[{"count":3,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/191\/revisions"}],"predecessor-version":[{"id":1164,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/191\/revisions\/1164"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=191"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=191"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=191"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}