This will be a joint session with the LLAMA seminar, with two speakers.<\/p>\n
Date and time: Wednesday, May 7th 2025, 15:00-18:00<\/p>\n
Venue: ILLC Seminar Room F1.15, Science Park 107 and<\/strong>\u00a0online<\/a>.<\/p>\n <\/p>\n First talk<\/span> (starting at 15:00) Speaker: Katsuhiko Sano<\/a> (Hokkaido University<\/a>)<\/p>\n Title: Craig Interpolation for Bi-intuitionistic Stable Tense Logic<\/strong><\/p>\n Abstract.<\/em> Bi-intuitionistic stable tense logic (BiSKt), introduced by Stell et al. (2016), provides a logical framework for mathematical morphology on graphs consisting of nodes and edges. In this talk, we establish the Craig interpolation theorem for BiSKt from a proof-theoretic perspective — that is, in terms of a sequent calculus for BiSKt. Although our sequent calculus is not cut-free, applications of the cut rule can be restricted to analytic ones — namely, those in which the cut formula is a subformula of the conclusion of the cut rule. To establish the Craig interpolation theorem for this calculus, we use a symmetric interpolation method originally proposed by Mints (2001) for the multi-succedent calculus of first-order intuitionistic logic. This method can be seen as a generalization of Maehara’s method. Our proof-theoretic approach also simplifies the method developed by Kowalski and Ono (2017) for proving the Craig interpolation theorem in bi-intuitionistic logic. This is a joint work with Hiroakira Ono (JAIST).<\/p>\n <\/p>\n Second talk<\/span> (starting at 16:30) Speaker: Alexander Kurz<\/a> (Chapman University<\/a>)<\/p>\n Title:\u00a0Quantale-Valued Modal Logic<\/strong><\/p>\n Abstract.<\/em> For applications of logic it is often desirable to have a common umbrella encompassing both classical discrete two-valued and quantitative continuous many-valued reasoning. What are principled ways to extend 2-valued modal logic to many-valued modal logic? What is a suitable generalization of Kripke semantics to this setting? This will be a joint session with the LLAMA seminar, with two speakers. Speaker: Katsuhiko Sano (Hokkaido University)
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\nWithout assuming knowledge of category theory, we will explain how category theory allows us to build a general framework to answer these questions. The key observation is that 2 is not only the familiar Boolean algebra but also an instance of a more general structure known as a quantale. A quantale is simply a complete lattice with a little extra structure. As observed by Lawvere in 1973, this extra structure allows us to extend ordinary 2-valued logic to a generalized logic that takes truth values in an arbitrary quantale. The models of such generalized logics encompass a variety of structures including metric spaces. In this talk, we will give a general introduction to this area of logic and also sketch some novel results about canonical extensions of fuzzy-algebras obtained in collaboration with Apostolos Tzimoulis.<\/p>\n","protected":false},"excerpt":{"rendered":"
\nDate and time: Wednesday, May 7th 2025, 15:00-18:00
\nVenue: ILLC Seminar Room F1.15, Science Park 107 and\u00a0online.
\n
\nFirst talk (starting at 15:00)<\/p>\n
\nTitle: Craig Interpolation for Bi-intuitionistic Stable Tense Logic
\nAbstract. Bi-intuitionistic stable tense logic (BiSKt), introduced by Stell et al. (2016), provides […]<\/p>\n","protected":false},"author":16,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-5341","post","type-post","status-publish","format-standard","hentry","category-all"],"_links":{"self":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/5341","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/comments?post=5341"}],"version-history":[{"count":8,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/5341\/revisions"}],"predecessor-version":[{"id":5425,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/5341\/revisions\/5425"}],"wp:attachment":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/media?parent=5341"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/categories?post=5341"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/tags?post=5341"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}