{"id":1618,"date":"2019-09-17T13:19:38","date_gmt":"2019-09-17T05:19:38","guid":{"rendered":"http:\/\/tsinghualogic.net\/JRC\/?p=1618"},"modified":"2019-09-17T13:19:40","modified_gmt":"2019-09-17T05:19:40","slug":"talk-exploring-the-core-logic-of-dependence-johan-van-benthem","status":"publish","type":"post","link":"http:\/\/tsinghualogic.net\/JRC\/talk-exploring-the-core-logic-of-dependence-johan-van-benthem\/","title":{"rendered":"[talk] Exploring The Core Logic of Dependence (Johan van Benthem)"},"content":{"rendered":"<blockquote><p>Time: 2019 September 27,\u00a013:30-16:00<br \/>\nVenue: \u8499\u6c11\u4f1f\u79d1\u6280\u5927\u697c\u5357\u697cS527, Tsinghua Univ.<\/p><\/blockquote>\n<p><strong>Speaker:<\/strong>\u00a0 Johan van Benthem (Stanford University)<\/p>\n<p><strong>Abstract<\/strong>:<\/p>\n<p style=\"padding-left: 40px;\">Dependence is a notion that pervades both ordinary\u00a0and scientific discourse. We present a decidable base\u00a0logic of functional dependence whose semantics uses\u00a0generalized assignment models for first-order logic.\u00a0This seminar is a survey and crash course in the topic.<\/p>\n<p style=\"padding-left: 40px;\">We determine the structural properties of dependence,\u00a0in analogy with those of abstract consequence relations,\u00a0and show how they fit with introducing explicit functional\u00a0definitions. Next, we discuss the philosophical significance\u00a0of this semantics, and then, using analogies with modal logic,\u00a0we go on to show completeness, decidability and other keyproperties of the core logic of dependence. For perspective,\u00a0we also indicate extensions in expressive power: e.g., the\u00a0core logic of independence turns out to be undecidable,\u00a0while natural dynamic extensions straddle the borderline\u00a0with undecidability. All these notions and results turn out\u00a0to extend naturally to a topological setting where a major\u00a0intuition of dependence is correlated approximability.<\/p>\n<p style=\"padding-left: 40px;\">Finally, we sketch how our logical perspective can also\u00a0incorporate richer notions of dependence found in data\u00a0bases, vector spaces, and strategic behavior in games.\u00a0If time permits, we will also make a few comparisons\u00a0with already existing systems of dependence logic.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Time: 2019 September 27,\u00a013:30-16:00 Venue: \u8499\u6c11\u4f1f\u79d1\u6280\u5927\u697c\u5357\u697cS5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/posts\/1618"}],"collection":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/comments?post=1618"}],"version-history":[{"count":3,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/posts\/1618\/revisions"}],"predecessor-version":[{"id":1621,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/posts\/1618\/revisions\/1621"}],"wp:attachment":[{"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/media?parent=1618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/categories?post=1618"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/tsinghualogic.net\/JRC\/wp-json\/wp\/v2\/tags?post=1618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}