次のレクチャーの予定をこのMLで流させていただきます。
岡田光弘(慶応義塾大学文学部哲学専攻)
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*ジラール教授(Jean-Yves GIRARD)連続講義 (9月25日、10月2日, Sept
25th,Oct.2nd, Keio Univ.)*
*Lecture**“LOGIC 2.0 : A derealistic refoundation of logic”
*
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参加自由、事前登録なしです。お気軽にお立ち寄りください。
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Abstract attached below アブストラクトは下をご覧ください。
1回目:9月25日(火) Sept.25th, 18:00-19:30, Lecture 1 and discussion.
2回目:10月2日(火) Oct.2nd, 17:00-19:00, Lecture 2 and extended
discussion,.
慶應義塾大学三田キャンパス 大学院校舎1階313番教室, Room 313 Graduate School
Building, Mita Campus, Keio University
(大学院校舎は下記キャンパスマップの8です)
Mita Campus, Keio University, Classroom 313, 1F of Graduate School Building
(Number 8 of the Campus Map below)
構内図Campus Map: https://www.keio.ac.jp/en/maps/mita.html
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招聘講師/ Invited Lecturer:
ジャン=イヴ ジラール 教授
(フランス国立科学センターCNRS名誉主任研究員、マルセイユ数学研究所)
Prof. Jean-Yves GIRARD (Directeur de Recherches émérite, CNRS-IMM)
題目/ Title:
LOGIC 2.0 : A derealistic refoundation of logic
See below for ABSTRACT (アブストラクトは下にあります。)
お問い合わせ先:
慶應義塾大学文学部 岡田光弘研究室
東京都港区三田2−15−45
Email(事務局): logic(a)abelard.flet.keio.ac.jp
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アブストラクト/ABSTRACT
LOGIC 2.0 : A derealistic refoundation of logic.
Logic is based upon a doubt as to « reality », not to speak of
authority. This is why axiomatic realism, a.k.a. Tarskism, at work in
familiar (1.0) logic is a miscarriage of logical rationality. We propose
to replace the trinity Syntax/Semantics/Meta, with an architecture based
upon the synthetic a posteriori : « l’usine » (the factory) and its
proofnets. We thus replace the nets of logic with the logic of nets.
Among the technical novelties, the self-dual propositional constants
フand ヲwhose multiplicative combinations define natural numbers. Since
equality becomes logical equivalence, natural numbers provide pairwise
contradictory propositions, which is classically inconsistent : a
conjunction can thus be true while one of its components is false.Truth,
which no longer proceeds from the Sky, is governed by the Euler-Poincaré
invariant of graphs, with a derealistic switch : the invariant depends
upon the divide between objective and subjective vertices. Derealism
thus accomplishes a spectacular jailbreak from Tarskism!
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皆様,
(重複して受け取られた場合はご容赦ください)
早稲田大学の藤原誠です.
9月10日(月)に早稲田大学早稲田キャンパスにてインスブルック大学の宮本賢治さんをお迎えしてセミナーを開催いたします.
ヨーロッパで研究をされている宮本さんの日本での貴重なご講演です.
参加自由ですのでどうぞふるってご参加下さい.
なお,今回の講演は英語で行われます.
予めご了承下さい.
詳細については以下のページをご参照下さい.
https://www.waseda.jp/inst/wias/news/2018/08/23/5646/
日時:2018年9月10日(月)16:00-17:30
Date & Time: Monday, 10 September 2018, 16:00 – 17:30
場所:早稲田大学早稲田キャンパス9号館5階第1会議室
Venue: Meeting room #1 on the 5th floor, Building #9, Waseda University
Speaker:
Kenji Miyamoto (University of Innsbruck, Kenji.Miyamoto(a)uibk.ac.at)
Title:
The epsilon calculus with equality predicate and Herbrand complexity
Abstract:
Hilbert's epsilon-calculus is based on an extension of the language of
predicate logic by a term-forming operator $\varepsilon$ [1]. Two
fundamental results about the epsilon-calculus, the first and second
epsilon theorem, play a role similar to that which the cut-elimination
theorem plays in sequent calculus. In particular, Herbrand's Theorem
is a consequence of the epsilon theorems. Moser and Zach study the
epsilon theorems and the complexity of the elimination procedure
underlying their proof, as well as the length of Herbrand disjunctions
of existential theorems obtained by this elimination procedure [2].
We extend their results to epsilon-calculus with equality predicate.
This is joint work with Georg Moser.
[1] D. Hilbert and P. Bernays,
Grundlagen der Mathematik, vol. 2, Springer Berlin, 1939.
[2] G. Moser and R. Zach,
The epsilon calculus and Herbrand complexity,
Studia Logica, vol. 82 (2006), no. 1, pp. 133--155.
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藤原 誠 (Makoto Fujiwara)
早稲田大学高等研究所
(Waseda Institute for Advanced Study, Waseda University)
E-mail: makoto_fujiwara(a)aoni.waseda.jp
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