[logic-ml] Talk by Petr Cintula (29 Oct 11:00-)

[Tetsuya Sato]

 (重複して受け取られた場合はご容赦ください)

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。
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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.