Kobe Colloquium on Logic, Statistics and Informatics
以下の要領でコロキウムを開催します。
日時:2013年2月6日(水)15:10-16:40
場所:神戸大学自然科学総合研究棟3号館4階421室(プレゼンテーション室)
講演者:Florian Pelupessy (Ghent)
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題目:Connecting the provable with the unprovable
アブストラクト:
Since Gödels famous incompleteness theorems it is well known that there exist theorems which are not provable in Peano Arithmetic. In the last decades of the last century many mathematically interesting examples of such unprovable statements emerged, for example: the Paris-Harrington theorem, the Kanamori-McAloon theorem, Kruskal's tree theorem, Hydra battles and Goodstein sequences. In these theorems it is possible to insert a parameter function, where the resulting theorem variant with constant parameter is provable, but the variant with as parameter the identity function is unprovable. An obvious question in these cases is at which threshold between those functions (ordered by eventual domination) the resulting theorem changes from provable to unprovable: the phase transition for provability of the theorem. We study these phase transitions with the goal of better understanding unprovability.
We will be examining the transition results for three Ramsey theorem variants: Friedman's adjacent Ramsey theorem, the Paris-Harrington theorem and the Kanamori-McAloon theorem. For these theorems it is possible to show a deep connection between lower/upper bound estimates for the variants with constant parameter values and the threshold values for the parametrised theorems. This shows an influence of mathematics which is provable at a level slightly stronger than exponential function arithmetic on provabiltiy at the level of Peano Arithmetic.
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交通:阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」
行きに乗車,「神大本部工学部前」停留所下車,徒歩すぐ.
http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm
連絡先:菊池誠 mkikuchi(a)kobe-u.ac.jp
Logic-ml の皆様,
以下の研究会の参加申込締切が迫ってまいり
ましたのでご案内させていただきます.
Computability Theory and Foundations of Mathematics (CTFM 2013)
(2013年2月18日(月)~2月20日(水),東京工業大学大岡山キャンパス)
参加ご希望の方は参加登録ページよりお申込ください.
http://sendailogic.math.tohoku.ac.jp/CTFM/registration.html
参加申込締切:2013年2月4日(月)
多くの方々の参加申込をお待ちいたしております.
江口直日,Sam Sanders, 田中一之
CTFM(a)math.tohoku.ac.jp
============================================================
Computability Theory and Foundations of Mathematics
(Tokyo Institute of Technology, Tokyo, Japan, February 18 - 20, 2013)
http://sendailogic.math.tohoku.ac.jp/CTFM/
============================================================
Computability Theory and Foundations of Mathematics (CTFM) aims to
develop computability theory and logical foundations of Mathematics.
The
scope involves the topics Computability Theory, Reverse Mathematics,
Nonstandard Analysis, Proof Theory, Constructive Mathematics, Theory of
Randomness and Computational Complexity Theory.
This is a successor workshop to Workshop on Proof Theory and
Computability Theory 2012 - Philosophical Frontiers in Reverse
Mathematics (February 20 - 23, 2012, Tokyo, Japan).
--------------------------------------------
Deadline of Registration: February 4th, 2013
--------------------------------------------
Invited Speakers:
Chi Tat Chong (National University of Singapore)
Erik Palmgren (Stockholm University)
Michael Rathjen (University of Leeds)
Helmut Schwichtenberg (LMU Munich)
Stephen G. Simpson (Pennsylvania State University)
Yang Yue (National University of Singapore)
Wu Guohua (Nanyang Technological University)
--------------------------------------------
Programme Committee:
Toshiyasu Arai (Chiba)
Naohi Eguchi (Tohoku)
Hajime Ishihara (JAIST)
Ryo Kashima (Tokyo Institute of Technology)
Sam Sanders (Ghent)
Kazuyuki Tanaka (Tohoku, Co-chair)
Andreas Weiermann (Ghent, Co-chair)
Takeshi Yamazaki (Tohoku)
Keita Yokoyama (Tokyo Institute of Technology)
--------------------------------------------
Eighth NII Type Theory Workshop
Date: February 6, 2013, 10:40--16:50
Place: National Institute of Informatics, Room 1904 (19th floor)
場所: 国立情報学研究所 19階 1904室
(半蔵門線,都営地下鉄三田線・新宿線 神保町駅または東西線 竹橋駅より徒歩5分)
(地図 http://www.nii.ac.jp/about/access/)
Program:
10:40--11:20 Toshihiko Uchida (The Graduate University for Advanced Studies)
Title: A Partial Translation from lambda U to lambda 2
11:20--12:00 Daisuke Kimura (National Institute of Informatics)
Title: Linear Pure Type Systems
12:00--14:00 Lunch Break
14:00--14:40 Kazuyuki ASADA (National Institute of Informatics)
Title: Curry-Howard Correspondence between Dialectica Interpretation
and Bidirectional Transformation
14:40--15:20 Makoto Tatsuta (National Institute of Informatics)
Title: Dual Calculus with Inductive and Coinductive Types
15:20--15:50 Tea Break
15:50--16:50 Stefano Berardi (Torino University)
Title: A Curry-Howard result for various subclassical logics
Abstracts:
----------------------------------------------------------------------
Toshihiko Uchida (The Graduate University for Advanced Studies)
Title: A Partial Translation from lambda U to lambda 2
Abstract: Girard showed that every type of sort * (i.e., proposition)
is inhabited in lambda U. Barendregt state without proof that every
type of sort Box (i.e., domain) is also inhabited in the system. In
this talk, we show that the second statement is not the case by giving
a partial translation from lambda U to lambda 2.
----------------------------------------------------------------------
Daisuke Kimura (National Institute of Informatics)
Title: Linear Pure Type Systems
Abstract: This talk proposes a linear variant of Pure Type Systems
(PTSs), called linear pure type systems (LPTSs). It is a general
framework, which provides a uniform way to treat various linear type
systems that have the features of linear logic. We first introduce a
subframework of LPTSs, called multiplicative linear pure type systems
(MLPTSs), in which only variables that linearly occur are
abstracted. All MLPTSs are consistent and satisfy strong
normalization. However their expressive power is rather weak. We then
give LPTSs by extending MLPTSs with exponentials. Each PTS can be
embedded into a LPTS. We also show the equivalence of strong
normalizability of PTSs and LPTSs by giving mutual translations
between them.
----------------------------------------------------------------------
Kazuyuki ASADA (National Institute of Informatics)
Title: Curry-Howard Correspondence between Dialectica Interpretation
and Bidirectional Transformation
Abstract: We give Curry-Howard style correspondence between
(propositional logic part of) Dialectica interpretation and
bidirectional transformation. Dialectica interpretation was
introduced by Godel to show relative consistency of Heyting Arithmetic
to System T. Independently, bidirectional transformation arose in
database community for automatic view-update problem, and recently
have been studied in programming language community to formulate
languages for bidirectional transformations. A bidirectional
transformation consists of a pair of forward ("usual") transformation
and a backward ("inverse") transformation, and we usually assume that
they satisfy some standard axioms called GetPut law and PutGet law. We
show GetPut law naturally fits the above correspondence to Dialectica
interpretation, and this gives a way of extending a language for
bidirectional transformations with GetPut law. Then we modify the
above scheme for PutGet law and the combination of GetPut and PutGet
laws. We also show that Paiva's variant of Dialectica model, GC,
corresponds to the category for inverse computation. Then for the
result by Paiva that the original Dialectica category is the coKleisli
category of some comonad on GC, we give similar result for PutGet law,
and we utilize this to investigate further categorical structures of
these models. Also we see that a kind of Diller-Nahm variant of
Dialectica interpretation corresponds to backward-partial
bidirectional transformation.
----------------------------------------------------------------------
Makoto Tatsuta (National Institute of Informatics)
Title: Dual Calculus with Inductive and Coinductive Types
Abstract: This talk gives an extension of Dual Calculus by
introducing inductive types and coinductive types. The same duality
as Dual Calculus is shown to hold in the new system, that is, this
talk presents its involution for the new system and proves that it
preserves both typing and reduction. The duality between inductive
types and coinductive types is shown by the existence of the
involution that maps an inductive type and a coinductive type to each
other. The strong normalization in this system is also proved.
First, strong normalization in second-order Dual Calculus is shown by
translating it into second-order symmetric lambda calculus. Next,
strong normalization in Dual Calculus with inductive and coinductive
types is proved by translating it into second-order Dual Calculus.
This is a joint work with Daisuke Kimura.
----------------------------------------------------------------------
Stefano Berardi (Torino University)
Title: A Curry-Howard result for various subclassical logics
Abstract: We introduce games with Sequential Backtracking as a model
for various sub-classical logic that have implication as a primitive
connective. We define a one-sided version of the logical systems,
whose proofs have a tree isomorphism (a kind of ``Curry Howard''
isomorphism) with respect to the winning strategies of the game
semantics. We use this correspondence to interpret various classical
proofs as learning algorithms.
----------------------------------------------------------------------
問合せ先 龍田 (tatsuta(a)nii.ac.jp)
みなさま
複数受け取られた場合はご容赦ください。
2月13日に京都大学で行われる CAPE Truth theory and Logic Workshop のご案内をご転送させて頂きます。
矢田部俊介
---------- Forwarded message ----------
CAPE Truth theory and Logic Workshopのお知らせ
皆様
京都大学大学院文学研究科附属応用哲学・倫理学教育研究センター(CAPE)の主催にて、
CAPE Truth theory and Logic Workshopが下記のように開催されます。
今回は特別講演として、ブリストル大学のPhilip Welch先生に、チューリングの
数学の業績に関する一般向け講演(元々は6'th European Cogress of Mathematics
で行われたもの)をお願いしました(1600-1745の最終枠です)。
専門家以外の方も、ぜひお越し下さい。
京都大学大学院文学研究科附属
応用哲学・倫理学教育研究センター
http://www.bun.kyoto-u.ac.jp/cape/cape-top_page/
事務補佐 竹中利彦
〒606-0085 京都市左京区吉田本町 京都大学文学部内
CAPE(a)bun.kyoto-u.ac.jp
****************************************************************************************
CAPE Truth theory and Logic Workshop
Date: February 13 (Wed) 9:00-17:00,
Place: The 8th lecture room, "Research Bldg. No. 2 (Sougou Kenkyu
2-Goukan)" of Kyoto University, No34 of the map in
http://www.kyoto-u.ac.jp/en/access/campus/main.htm (京都大学総合研究2号館第8講義室)
CAPE Website:
http://www.bun.kyoto-u.ac.jp/cape/cape-top_page/
Timetable:
9:00-10:15 Shunsuke Yatabe "Yablo paradox and semantics of coinductive language"
10:30-11:45 Graham E. Leigh "Global reflection and theories of truth"
13:15-14:30 Katsuhiko Sano "What is the corresponding first-order
logic to coalgebraic modal logic?"
14:30-15:45 Leon Horsten " One hundred years of semantic paradox"
16:00-17:15 Philip Welch "Alan Turing's Mathematical work"
Abstracts:
Shunsuke Yatabe (Kyoto University)
title: Yablo paradox and semantics of coinductive language
Abstract:
We generalize the framework of Barwise and Etchmendy's "the
liar" to that of coinductive language, and focus on a difficulty of
constructing semantics. We define a game theoretic semantics, which can
be regarded as a version of Austin semantics.
Graham E. Leigh (University of Oxford)
title: Global reflection and theories of truth
Abstract:
This talk explores the relationship between the global reflection
principle ("If A is provable, A is true") and its arithmetic cousins
("If A is provable then A"). I will provide a proof-theoretic analysis
of a number of axiomatic theories of truth expanded by transfinite
hierarchies of reflection principles.
Katsuhiko Sano (School of Information Science, Japan Advanced
Institute of Science and Technology)
title: What is the corresponding first-order logic to coalgebraic modal logic?
Abstract:
It is well-known that modal logic over Kripke models can be
regarded as the bisimulation-invariant fragment of first-order logic,
where the notion of bisimulation tells us when given two Kripke models
are `similar' with each other. This is called Van Benthem's
characterization theorem. The main aim of this talk is to propose a
corresponding first-order syntax with Van Benthem-style
characterization to coalgebraic modal logic, a uniform framework to
cover modal logic over Kripke models, modal logic over neighborhood
models, graded modal logic, probabilistic modal logic, etc. This talk
focuses on a conceptual background to explain our strategy of finding
a corresponding FO syntax for coalgebraic modal logic. A key idea
consists in Arthur Prior's early idea of hybrid logic (esp. modal
operators for pointed truth) and C. C. Chang's FO syntax for
neighborhood models. This talk is based on a joint work with Dirk
Pattinson (ANU), Tadeusz Litak (Friedrich-Alexander University of
Erlangen and Nuremberg (FAU)), and Lutz Schroeder (FAU).
Leon Horsten (University of Bristol)
title: One hundred years of semantic paradox
Abstract:
This article contains an overview of the main problems, themes and
theories relating to the semantic paradoxes in the twentieth century.
From this historical overview I tentatively draw some lessons about
the way in which the field may evolve in the next decade.
Philip Welch (University of Bristol)
title: Alan Turing's Mathematical work
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