Kisoron-ml June 2016

2 participants
3 discussions

JAIST Logic Seminar Series
by Hajime Ishihara 28 Jun '16

28 Jun '16

皆様ジェノヴァ大学のEugenio Moggi先生の特別集中講演のお知らせです。どうぞふるってご参加ください。問合せ先：石原　哉北陸先端科学技術大学院大学情報科学系 e-mail: ishihara(a)jaist.ac.jp ----------------------------------------------- * JAIST Logic Seminar Series * * This series of lectures is held as a part of JSPS Core-to-Core Program, A. Advanced Research Networks, and EU FP7 Marie Curie Actions IRSES project CORCON. (http://www.jaist.ac.jp/logic/ja/core2core, https://corcon.net/) Dates: Tuesday 2 August, 2016, 13:30-15:10 Thursday 4 August, 2016, 13:30-15:10 Friday 5 August, 2016, 10:50-12:30 Place: JAIST, Collaboration room 7 (I-56) (Access: http://www.jaist.ac.jp/english/location/access.html) Speaker: Eugenio Moggi (University of Genova) *Tuesday 2 August, 2016, 13:30-15:10* LECTURE 1: Categories of Classes for Collection Types ABSTRACT. Collection types have been proposed by Buneman and others (in the '90) as a way to capture database query languages in a typed setting. In 1998 Manes introduced the notion of collection monad on the category S of sets as a suitable semantics for collection types. The canonical example of collection monad is the finite powerset monad Pf. In order to account for the algorithmic aspects of database languages, the category S is unsuitable, and should be replaced with other categories, whose arrows are maps computable by "low complexity" algorithms. We propose "realizability for DSL" (Domain Specific Languages), where the starting point is a monoid C of endomaps on a set D, instead of a combinatory algebra on D, as a way to get such categories by constructions like the category A[C] of "assemblies". To get Pf in a systematic way we borrow ideas from AST (Algebraic Set Theory, started by Joyal and Moerdijk in the '90), where they fix a notion of "small" map in a category of "classes", and read "small" as "finite". *Thursday 4 August, 2016, 13:30-15:10* LECTURE 2: Hybrid System Trajectories as Partial Continuous Maps ABSTRACT. Hybrid systems (HS) are dynamic systems that exhibit both continuous and discrete dynamic behavior: they can flow (according to a differential equation) and jump (according to a transition relation). HS can be used for modeling rigid body dynamics with impacts, and more generally Cyber-Physical Systems. HS can exhibit Zeno behaviors, that arise naturally in rigid body dynamics with impacts, but are absent from purely discrete or purely continuous systems. Dealing properly with these behaviors is a prerequisite to give sound definitions of concepts such as reachability. We propose the use of partial continuous maps (PCM) as trajectories that describe how a HS evolves over time. PCMs enable a notion of trajectory that can go beyond Zeno points. *Friday 5 August, 2016, 10:50-12:30* LECTURE 3: Models, Over-approximations and Robustness ABSTRACT. Hybrid systems, and related formalisms, have been successfully used to model Cyber- Physical Systems. The usual definition of "reachability", in terms of the reflexive and transitive closure of a transition relation, is unsound for Zeno systems. We propose "safe reachability", which gives an over-approximation of the set of states that are "reachable in finite time" from a set of initial states. Moreover, mathematical models are always a simplification of the system they are meant to describe, and one must be aware of this mismatch, when using these models for system analyses. In safety analysis it is acceptable to use over-approximations of the system behavior, indeed they are the bread and butter of counterexample guided abstraction refinement (CEGAR). We propose a notion of safe (time-bounded) reachability, which is also robust wrt arbitrary small overapproximations, and argue that it is particularly appropriate for safety analysis.

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分科会便りに掲載する情報（７月８日（金）しめきり）
by Toshio Suzuki 17 Jun '16

17 Jun '16

数学基礎論および歴史分科会の皆様　　分科会便りに掲載する情報（７月８日（金）しめきり）お世話になっております．首都大学東京の鈴木登志雄です．評議員からの連絡です．数学通信２１巻２号（８月２２日発送予定）に会報１６２号が掲載されます．その中の分科会便りに掲載希望のお知らせがありましたら，２０１６年７月８日（金）までに，鈴木 toshio-suzuki[atmark]tmu.ac.jp へご連絡ください．編集部に掲載を依頼するかどうかの最終判断は評議員にご一任ください．文章の軽微な修正を評議員・編集部が行う場合がありますのでご了承ください．過去の会報は以下の場所でご覧になれます． http://mathsoc.jp/section/logic_and_history/Tayori.html 話は変わりますが，秋季総合分科会の一般講演申込期間は　　６月２４日（金）までです． http://mathsoc.jp/meeting/kansai16sept/ ６月１７日（金）１７：３０頃の一般講演申込み状況は，仮申込み中のご講演を含めて以下の通りです．歴史４件，基礎論８件，計１２件申込みしてくださった皆様，ありがとうございます．まだ１週間ありますので，まだの方もふるってお申し込みください． -- 鈴木登志雄首都大学東京理工学研究科数理情報科学専攻 toshio-suzuki(a)tmu.ac.jp

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JAIST Logic Seminar Series
by Hajime Ishihara 08 Jun '16

08 Jun '16

皆様オークランド大学のBakhadyr Khoussainov先生の講演のお知らせです。どうぞふるってご参加ください。問合せ先：石原　哉北陸先端科学技術大学院大学情報科学系 e-mail: ishihara(a)jaist.ac.jp ----------------------------------------------- * JAIST Logic Seminar Series * Date: Monday 20 June, 2016, 15:20-17:00 Place:JAIST, Collaboration room 7 (I-56) (Access: http://www.jaist.ac.jp/english/location/access.html) Speaker: Bakhadyr Khoussainov (University of Auckland) Title: Computably Enumerable Structures: Domain dependency Abstract: Computably enumerable structures arise naturally in algebra and computer science. In algebra examples include finitely presented universal algebras such as finitely presented groups. In computer science, these are abstract data types defined by equational or quasi-equational specifications. The domains of these algebraic structures are quotient sets of the form $\omega/E$, where $\omega$ is the set of natural numbers and $E$ is a computably enumerable (c.e.) equivalence relations. We consider c.e. structures whose domains are of the form $\omega/E$ and study various properties of these structures and their dependence on the domain $\omega/E$

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Kisoron-ml June 2016