皆様
6月13日(木)に北陸先端科学技術大学院大学で行われます
Baaz 教授、Gamsakhurdia 氏(ウィーン工科大学)の講演のお知らせです。
皆様、どうぞ奮ってご参加ください。
廣川 直 (JAIST)
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* JAIST Logic Seminar Series *
Date:
June 13 (Thu), 2024, 15:30 - 17:10
Place:
I-57g (seminar room on 5F of IS Building III) at JAIST
(Access: https://www.jaist.ac.jp/english/top/access/index.html)
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Quantifier shifts
M. Baaz, Vienna University of Technology
(joint work with J. Aguilera, M. Gamsakhurdia, R. Jalali)
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Abstract:
In this lecture we analyze the operation of quantifier shifts,
one of the oldest deduction formalism in logic. Quantifier shifts are
orthogonal to usual deduction rules and have a considerable impact
on the complexity of proofs. To understand them better a variant
of sequent calculus with relaxed Eigenvariable conditions is developed,
which is able to represent quantifier shifts in a cut-free format.
There is a non-elementary speed-up of cut-free proofs in the new format
vs cut free proofs in the usual format, a manifestation of the
proof-theoretic power of quantifier shifts.
The intuitionistic version of this calculus is applied to prove, that
an intermediary logic admits Standard Skolemization iff it admits all
classical quantifier shifts.
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The Limits of Prenexation in First-order Gödel Logics
Mariami Gamsakhurdia, Vienna University of Technology
(joint work with Matthias Baaz)
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Abstract:
One of the first recognised characteristics of classical logic is the
existence of a prenex form for each formula. The quantifier-shifting rules
are used non-uniquely to construct these prenex forms. The expressive power
of prenex fragments is easy to see in classical logic because it coincides
with the whole logic, and in Intuitionistic logic since the prenex formulas
are very weak (the validity of the prenex formula is decidable). However,
because Gödel logics are intermediary logics, the expressibility of its
prenex is relatively important.
It is clear that prenex normal forms cannot be constructed in the usual
sense in Gödel logics because some of the quantifier-shift rules may fail,
but this does not imply that no prenex normal form exists. However,
demonstrating that such prenex forms do not exist is more difficult.
Prenexation does not work for \(G_{[0,1]}\) when $0$ is not isolated, since
the formula \((\neg \forall x A(x)\wedge \forall x \neg \neg A(x))\) does
not allow a prenex normal form. To prove this fact, we use a glueing
argument. This result can be extended to all Gödel logics where there is
one accumulation point from above, even if it is not $0$.
In this talk we provide the complete classification for the first-order
Gödel logics with respect to the property that the formulas admit logically
equivalent prenex normal forms. We show that the only first-order Gödel
logics that admit such prenex forms are those with finite truth value sets
since they allow all quantifier-shift rules and the logic \(G_\uparrow\)
with only one accumulation point at $1$. In all the other cases, there are,
in general, no logically equivalent prenex normal forms. We will also see
that \(G_\uparrow\) is the intersection of all finite first-order Gödel
logics.
The second stage of our research investigates the existence of the validity
equivalent prenex normal form. Gödel logics with a finite truth value set
admit such prenex forms. Gödel logics with an uncountable truth value set
have the prenex normal form if and only if every surrounding of \(0\) is
uncountable or \(0\) is an isolated point. Otherwise, uncountable Gödel
logics are incomplete, and the prenex fragment is always complete with
respect to the uncountable truth value set. Therefore, there is no
effective translation to the valid formula and the valid prenex form. The
countable case, however, is still up for debate.
References
Matthias Baaz, Norbert Preining
Gödel-Dummett logics, in: Petr Cintula, Petr Hájek, Carles Noguera (Eds.),
Handbook of Mathematical Fuzzy Logic vol. 2, College Publications, (2011),
pp. 585–626, chapter VII.
Matthias Baaz, Norbert Preining, Richard Zach
First-order Gödel logics, Annals of Pure and Applied Logic vol. 147. (2007)
pp. 23–47.
次のご案内をさせていただけると幸いです。
慶應大 岡田光弘 峯島宏次
ーーーーーーーーーーーーーーーーーーー
論理―計A算―哲学セミナーLogic-Computation-Philosophy Seminar
「プログラム」「アルゴリズム」「計算モデル」を「定義する」ことに関する
Prof. Thomas Seillerの講義をご案内させていただきます。
ハイブリッド形式
講義Title« Defining "program", "algorithm", and "model of computation" —
including a discussion on how models of linear logic emerge by generalizing
geometry of interaction and transcendental syntax constructions »
We will put updated information in any, here.最新情報URL
https://abelard.flet.keio.ac.jp/2024/seminar_talk_202405
<https://abelard.flet.keio.ac.jp/satellite-workshop_202406/poster_ja.pdf>
5月28日火曜日 17:30-19:00 May 28 Thuesday
慶應義塾大学三田キャンパス東館(東門の建物)4階オープンラボ
三田キャンパス:アクセス:[慶應義塾] (keio.ac.jp) <https://www.keio.ac.jp/ja/maps/mita.html>
キャンパスマップ13番
At the Open-Lab, 4th floor of the East (Research) Building at the East Gate
of Mita-Campus of Keio University
Mita Campus: Keio University <https://www.keio.ac.jp/en/maps/mita.html>
Building # 13 on the Campus Map
要事前登録・Preregistration required
登録用のリンク Hybrid Meeting
https://forms.gle/cbPr2vQrJA4haVFW7
Speaker:Thomas Seiller -(CNRS-LIPN, IHPST)
Title of the Talk
« Defining "program", "algorithm", and "model of computation" — including
a discussion on how models of linear logic emerge by generalizing geometry
of interaction and transcendental syntax constructions »
Abstract:
What is a model of computation? What is a program, an algorithm? While
theoretical computer science has been founded on computability theory, the
latter does not answer these questions. Indeed, it is a mathematical theory
of computable functions, and does not account for computation itself. A
symptomatic consequence is the notion of Turing-completeness. This standard
(sole?) equivalence between models of computation is purely extensional: it
does only care about what is computed and not how, blind to complexity
aspects and the question of algorithmic completeness. More importantly, the
theory of computation is continuously growing further from how actual
machines compute.
I will present a proposal for alternative foundations more faithful to
computer science practice and interests. This mathematisation of computer
science is grounded within the theory of dynamical systems, focussing on
*how* computation is performed rather than only on *what* is computed. I
will argue that it generalises computability theory while still allowing to
recover standard results.
This point of view can be used to:
provide a uniform account of several lower bounds from algebraic complexity
and strengthen them
define static analysis methods which can be implemented in usable tools
define families of linear realisability models (realisability models for
linear logic)
lead to a semantic approach of implicit computational complexity
propose a formal definition of the notion of algorithm
In this talk, I will focus on two aspects from this list, namely points 3
and 5:
First, I will explain how abstract programs give rise to models of
(fragments of) linear logic, generalising Jean-Yves Girard’s geometry of
interaction (or more recent transcendental syntax) constructions. I will
also explain how these technical developments shed a new light on the
question of defining logical constants.
Second, I will present the formal definition of algorithm that stems from
the approach, discuss its properties and provide a few examples.
問い合わせ先Logic-Computation-Philosophy Group, Dept. Philoophy Keio Univ
logic[AT]abelard.flet.keio.ac.jp 岡田光弘 峯島宏次
皆様,
京都大学の池渕です.APLAS 2024のfinal CfPをお送りします.
Submission deadlineが延期され,5/31(金)になりました.
======================================================
Final CFP: Deadline extended till May 31
APLAS 2024 -- The 22nd Asian Symposium on Programming Languages and Systems
October 22-24, 2024, Kyoto, Japan
https://conf.researchr.org/home/aplas-2024/ <https://conf.researchr.org/home/aplas-2024/>
APLAS 2024 aims to bring together programming language researchers,
practitioners and implementors *worldwide*, to present and discuss the
latest results and exchange ideas in all areas of programming
languages and systems. APLAS 2024 is co-located with the
22nd International Symposium on Automated Technology for Verification
and Analysis (ATVA).
We solicit submissions in the form of regular research papers
describing original scientific research results, including system
development and case studies. Among others, solicited topics include:
programming paradigms and styles; methods and tools to specify and
reason about programs and languages; programming language foundations;
methods and tools for implementation; concurrency and distribution;
applications, case studies and emerging topics.
Submissions should not exceed 17 pages, excluding bibliography, in the
Springer LNCS format. The reviewing process is light double-blind,
with a rebuttal phase to address factual errors and minor
misunderstandings.
Proceedings of APLAS 2024 will be published by Springer as part of
Lecture Notes in Computer Science (LNCS).
https://link.springer.com/conference/aplas <https://link.springer.com/conference/aplas>
APLAS 2024 continues the tradition of the best paper award.
Submission deadline: Fri May 31 (EXTENDED, firm)
Response period: Jul 24-26
Acceptance notification: Fri Aug 2
Camera-ready: Sat Aug 31
The submission website is now open: https://aplas24.hotcrp.com/ <https://aplas24.hotcrp.com/>
General Chair: Jacques Garrigue (Nagoya U.)
Publicity Chairs: Ryosuke Sato (TUAT U.), Mirai Ikebuchi (Kyoto U.)
Program Committee:
Beniamino Accattoli (Inria & Ecole Polytechnique)
Pierre-Evariste Dagand (IRIF / CNRS)
Silvia Ghilezan (University of Novi Sad, Mathematical Institute SASA)
Fritz Henglein (DIKU and Deon Digital)
Mirai Ikebuchi (Kyoto University)
Patrik Jansson (Chalmers University of Technology and University of Gothenburg)
Oleg Kiselyov (Tohoku University, PC Chair)
Hsiang-Shang ‘Josh’ Ko (Academia Sinica)
Daan Leijen (Microsoft Research)
Martin Lester (University of Reading)
Fredrik Nordvall Forsberg (University of Strathclyde)
Matija Pretnar (University of Ljubljana)
Peter Schachte (The University of Melbourne)
Sven-Bodo Scholz (Radboud University)
Philipp Schuster (University of Tübingen)
Taro Sekiyama (NII)
Amir Shaikhha (University of Edinburgh)
Pavle Subotic (Fantom Foundation)
Yong Kiam Tan (Institute for Infocomm Research, A*STAR)
Kazunori Ueda (Waseda University)
Yuting Wang (Shanghai Jiao Tong University)
Ki Yung Ahn (Hannam University)