{"id":490,"date":"2014-10-28T08:45:58","date_gmt":"2014-10-28T07:45:58","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?page_id=490"},"modified":"2017-10-05T09:43:03","modified_gmt":"2017-10-05T08:43:03","slug":"mvl","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/490-mvl\/","title":{"rendered":"MVL"},"content":{"rendered":"<h1 style=\"text-align: center;\">Course on Many-Valued Logics (Autumn 2014)<\/h1>\n<p><center>This page concerns the course `Many-Valued Logics&#8217;, taught at the University of Amsterdam from September\u00a0&#8211; October\u00a02014.\u00a0<\/center><\/p>\n<h2>Contents of the\u00a0page<\/h2>\n<ul>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#news\">News<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#contents\">Contents of the classes<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#material\">Course material<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#prac\">Practicalities<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#grading\">Grading and homework assignments<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/mvl\/#course\">Course Description and Prerequisites<\/a><\/li>\n<\/ul>\n<h2><a name=\"contents\"><\/a>Contents<\/h2>\n<p>The course\u00a0covers the following topics:<\/p>\n<ul>\n<li>Basic Logic and Monoidal t-norm Logic.<\/li>\n<li>Substructural logics and residuated lattices.<\/li>\n<li>Cut elimination and completions.<\/li>\n<li>Lukasiewicz logic.<\/li>\n<\/ul>\n<p>More specifically, this\u00a0is the content of each\u00a0single class:<\/p>\n<ul>\n<li><strong>September, 1:<\/strong> Introduction, motivations, t-norms and their residua. Section 2.1 (up to Lemma 2.1.13) of the Course Material 1.<\/li>\n<li><strong>September, 5:<\/strong> Basic Logic, Residuated lattices, BL-algebras, linearly ordered BL-algebras. Section 2.2 and 2.3 (up to Lemma 2.3.16) of the Course Material 1.<\/li>\n<li><strong>September, 8:<\/strong> Lindenbaum-Tarski algebra of BL, algebraic completeness. Monodical t-norm logic, MTL-algebras, standard completeness. The rest of Course Material 1 (excluding Section 2.4) and Course Material 2.<\/li>\n<li><strong>September, 12:<\/strong>\u00a0Ordinal decomposition of BL-algebras. Mostert and Shield Theorem. \u00a0Course Material\u00a03.<\/li>\n<li><strong>September, 15:<\/strong>\u00a0Ordinal decomposition of BL-algebras (continued). Algebrizable logics and equivalent algebraic semantics. \u00a0Course Material\u00a04.<\/li>\n<li><strong>September, 19:<\/strong> Algebrizable logics and equivalent algebraic semantics (continued). \u00a0Course Material\u00a04.<\/li>\n<li><strong>September, 22:<\/strong> Algebrizable logics and equivalent algebraic semantics (continued): Leibniz operator and implicit characterisations of algebraizability. \u00a0Course Material\u00a04.<\/li>\n<li><strong>September, 26:<\/strong> Leibniz operator and implicit characterisations of algebraizability (continued). \u00a0Course Material\u00a04. Gentzen calculus and the substructural hierarchy. Course Material\u00a05 (to be continued).<\/li>\n<li><strong>September, 29:<\/strong> Structural quasi-equations and $N_2$ equations. Residuated frames. Course Material\u00a05 (Continued).<\/li>\n<li><strong>October, 3:<\/strong> Analytic quasi-equations, dual frames, and MacNeille completions. Course Material\u00a05 (Continued).<\/li>\n<li><strong>October, 9:<\/strong>\u00a0Atomic conservativity, closing the circle of equivalencies. Course Material\u00a05 (Continued).<\/li>\n<li><strong>October, 10:<\/strong>\u00a0Lukasiewicz logic and MV-algebras. Mundici&#8217;s equivalence.\u00a0Course Material 6.<\/li>\n<li><strong>October, 17:<\/strong>\u00a0The duality between semisimple MV-algebras and Tychonoff spaces.\u00a0Course Material 7.<\/li>\n<\/ul>\n<h2><a name=\"material\"><\/a>Course material<\/h2>\n<p>The material needed during the course can be found below.<\/p>\n<ul>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM1.pdf\">Course material 1<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM2.pdf\">Course material 2<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM3.pdf\">Course material 3<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM4.pdf\">Course material 4<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM5.pdf\">Course material 5<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/MVLcourse\/CM6.pdf\">Course material 6<\/a><\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/duality-revised.pdf\">Course material 7<\/a><\/li>\n<li>An example of a possible final exam can be <a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/exam.pdf\">downloaded here<\/a>.<\/li>\n<\/ul>\n<p>The homework due during the course can be found below.<\/p>\n<ul>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw1.pdf\">Homework 1<\/a>\u00a0(Deadline 12th September)<\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw2.pdf\">Homework 2<\/a>\u00a0(Deadline 19th September)<\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw3.pdf\">Homework 3<\/a>\u00a0(Deadline 26th September)<\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw4.pdf\">Homework 4<\/a>\u00a0(Deadline 3d October)<\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw5.pdf\">Homework 5<\/a>\u00a0(Deadline 10th October)<\/li>\n<li><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/hw6.pdf\">Homework 6<\/a>\u00a0(Deadline 17th October)<\/li>\n<\/ul>\n<h2><a name=\"prac\"><\/a>Practicalities<\/h2>\n<h3>Staff<\/h3>\n<ul>\n<li>Lecturer:\u00a0<a href=\"mailto:luca.spada@gmail.com\">Luca Spada<\/a><\/li>\n<\/ul>\n<h3>Dates\/location:<\/h3>\n<ul>\n<li>Classes run from the 1st of September\u00a0until the 17th of October; there will be 14 classes in total.<\/li>\n<li>There are two classes weekly.<\/li>\n<li>Due to the high number of participants classrooms will change weekly, <a href=\"http:\/\/www.datanose.nl\">datanose.nl<\/a> will always be updated with the right classrooms.<\/li>\n<\/ul>\n<h2><a name=\"grading\"><\/a>Grading and homeworks<\/h2>\n<ul>\n<li>The grading is on the basis of weekly homework assignments, and a written exam at the end of the course.<\/li>\n<li>The\u00a0homework assignments will be made available weekly through this page.<\/li>\n<li>The final grade will be determined for 2\/3 by homeworks, and for 1\/3 by the final exam.<\/li>\n<li>In order to pass the course, a score at least 50\/100 on the final exam is needed.<\/li>\n<\/ul>\n<h3>More specific information about homework and grading:<\/h3>\n<ul>\n<li>You are allowed to collaborate on the homework exercises, but you need to acknowledge explicitly with whom you have been collaborating, and write the solutions independently.<\/li>\n<li>Deadlines for submission are strict.<\/li>\n<li>Homework handed in after the deadline may not be taken into consideration; at the very least, points will be subtracted for late submission.<\/li>\n<li>In case you think there is a problem with one of the exercises, contact the lecturer immediately.<\/li>\n<\/ul>\n<h2><a name=\"course\"><\/a>Course Description<\/h2>\n<p>Many-valued logics are logical systems in which the truth values may be more than just &#8220;absolutely true&#8221; and &#8220;absolutely false&#8221;. This simple loosening opens the door to a large number of possible formalisms. The main methods of investigation are algebraic, although in the recent years the proof theory of many-valued logics has had a remarkable development.<\/p>\n<p>This course will address a number of questions regarding classification, expressivity, and algebraic aspects of many-valued logics. Algebraic structures as Monoidal t-norm based algebras, MV-algebras, and residuated lattices will be introduced and studied during the course.<\/p>\n<p>The course will cover seclected chapters of the following books.<\/p>\n<ul>\n<li>P. H\u00e1jek, &#8216;<em>Metamathematics of Fuzzy Logic<\/em>&#8216;, Trends in Logic, Vol. 4\u00a0Springer, 1998.<\/li>\n<li>P. Cintula, P. H\u00e1jek, C. Noguera (Editors). &#8216;<em>Handbook of Mathematical Fuzzy Logic<\/em>&#8216; &#8211; Volume 1 and 2. Volumes 37 and 38 of Studies in Logic, Mathematical Logic and Foundations. College Publications, London, 2011<\/li>\n<li>R. L. O. Cignoli, I. M. L. D&#8217;Ottaviano e D. Mundici, &#8216;<em>Algebraic Foundations of Many-Valued Reasoning<\/em>&#8216;, Trends in Logic, Vol. 7\u00a0Springer, 2000<\/li>\n<li>D. Mundici. &#8216;<em>Advanced Lukasiewicz calculus and MV-algebras<\/em>&#8216;, Trends in Logic, Vol. 35 Springer, 2011.<\/li>\n<\/ul>\n<h3>Prerequisites<\/h3>\n<p>It is assumed that students entering this class possess<\/p>\n<ul>\n<li>Some mathematical maturity.<\/li>\n<li>Familiarity with the basic theory of propositional and first order (classical) logic.<\/li>\n<\/ul>\n<p>Basic knowledge of general algebra, topology and category theory will be handy but not necessary.<\/p>\n<p>&nbsp;<\/p>\n<p><center><strong>Comments, complaints, questions<\/strong>: mail\u00a0<a href=\"mailto:luca.spada@gmail.com\">Luca Spada<\/a><\/center><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Course on Many-Valued Logics (Autumn 2014) This page concerns the course `Many-Valued Logics&#8217;, taught at the University of Amsterdam from September\u00a0&#8211; October\u00a02014.\u00a0 Contents of the\u00a0page News Contents of the classes Course material Practicalities Grading and homework assignments Course Description and Prerequisites Contents The course\u00a0covers the following topics: Basic Logic and Monoidal t-norm Logic. Substructural logics [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[15,31,35,40,64,14,28,75,29,37],"class_list":["post-490","post","type-post","status-publish","format-standard","hentry","category-teaching","tag-amsterdam","tag-categorical-duality","tag-changs-completeness-theorem","tag-course","tag-free-algebra","tag-illc","tag-lukasiewicz-logic","tag-many-valued-logic","tag-mv-algebras","tag-rational-polyhedra"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/490","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=490"}],"version-history":[{"count":59,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/490\/revisions"}],"predecessor-version":[{"id":1142,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/490\/revisions\/1142"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=490"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=490"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=490"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}