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京都大学数理解析研究所の佐藤です。
10月29日11:00から、チェコ科学アカデミーのPetr Cintula氏に 以下の講演をしていただくことになりましたので、 ご連絡いたします。どうぞお気軽にお越しください。 ========== Time: 11:00-12:00, 29 Oct, 2015 Place: Rm 478, Research Building 2, Main Campus, Kyoto University 京都大学 本部構内 総合研究2号館 4階478号室 http://www.kyoto-u.ac.jp/en/access/yoshida/main.html (Building 34) http://www.kyoto-u.ac.jp/ja/access/campus/map6r_y.htm (34番の建物)
Speaker: Petr Cintula (The Czech Academy of Sciences)
Title: Logic and mathematics with lattice-valued predicates
Abstract: Classical predicate logic interprets n-ary predicates as mappings from the n-th power of a given domain into the two-valued boolean algebra 2. The idea of replacing 2 by a more general structure is very natural and was shown to lead to a very interesting mathematics: prime examples are the boolean-valued or Heyting-valued models of set theory (or even more general models proposed by Takeuti & Titani (1992), Titani (1999), and Hajek & Hanikova (2001)).
In the first part of the talk we present a framework for the study of logics where predicates can take values in a lattice (with additional operators) from a given class satisfying certain minimal conditions (our framework covers previous approaches of Rasiowa & Sikorski (1963), Horn (1969), Rasiowa (1974), Hajek (1998), and others). For each such logic we first describe its `propositional' part and then use it to give an axiomatization of the full first-order logic.
The second part of the talk shows that the proposed logical formalism is rich enough to support non-trivial mathematical theories. We illustrate it by proving `graded' variant of the well-know relation between equivalences and partitions. The goal of the example is to illustrate the contrast between very general semantical interpretation of the proven fact and its almost classical proof.
logic-ml@fos.kuis.kyoto-u.ac.jp