Call for Participation!
5th ALGI in Chiba

• 日程 Jan. 29 and 30, 1998
• 場所 千葉大学 (けやき会館2階会議室1) 交通案内
• Program(tentative)
  • 1/29 Session I(14:30〜16:30)
    1. 木下 佳樹 (電総研)
       Title: Sketches
       Abstract: This is a joint work with J. Power and M. Takeyama. We generalise the notion of sketch. For any locally finitely presentable category, one can speak of algebraic structure on the category, or equivalently, a finitary monad on it. For any such finitary monad, we define the notions of sketch and strict model and prove that any sketch has a free strict model on it. This is all done with enrichment in any monoidal biclosed category that is locally finitely presentable as a closed category. Restricting our attention to enrichment in Cat, we mildly extend the definition of strict model to give a definition of model, and we prove that every sketch has a free model on it. The leading example is the category of small categories together with the monad for small categories with finite products: we then recover the usual notions of finite product sketch and model; and that is typical. This generalises many of the extant notions of sketch.
    2. 磯部 祥尚 (電総研)
       Title: A synthesis method of loose specifications from requirements
       Authors: Yoshinao ISOBE, Yutaka SATO, Kazuhito OHMAKI
       Abstract: In this talk, we present a CCS-like specification language called MSPEC for describing loose specifications, where each loose specification can represent two or more specifications. And then, we present a method to synthesize a loose specification from two given requirements. The synthesized loose specification represents all the specifications satisfying both the requirements and is called the principal specification of the requirements. We can recursively use the method for synthesizing the principal specifications of three or more requirements.
  • Business Meeting(16:30〜16:50)
  • 1/30 Session II(10:30〜12:30)
    3. 桜井 貴文 (千葉大)
       Title: Substructural Logic の Kripke Semantics について
       Abstract: [Ono: Semantics for Substructural Logics] では full Lambek logic (exchangeのないlinear logic) に対してFL-algebraによるsemanticsと so-monoidによるKripke semanticsが定義されている。propositionalな場合の 両者の関係は、[Ono,Komori: Logics without the Contraction Rule] におい て BCC/BCK logic に対して述べられているfilterによる構成法を使って記述 できる。ここではその構成法をmodal operator ! ? が加わった場合に拡張す る。ここで使う構成法はGirardがmonoidからphase spaceを構成するときに使っ た構成法(の非可換かつ直観主義版)である。また直観主義S4のsemanticsとの 関連も考える。
    4. 白旗 優 (慶応大)
       Title: The phase-valued model of a ZF-style linear set theory (予定)
       Abstract: 古典論理での ZF集合論に対するブール価モデルは、 直観主義論理や量子論理に拡張されているが、この講演では phase-space を使うことで、線形論理へのその拡張を試みる。
  • 1/30 Session III(13:30〜15:30)
    5. 赤間 陽二 (東大)
       Title: A Freyd-Scedrov's Allegory of The Tarski's Relation Algebra
       Abstract: Because the pairing operation of set can be subtle in a set theory such as Quine's New Foundation, the binary relations are concerned for a foundational study of sets. An allegory, introduced by Freyd and Scedrov, is a category formulating binary relations over heterogeneous sets, while the relational algebra, introduced by Tarski, is an algebraic formulation of binary relations over homogeneous sets. Recently, they are applied to program transformation of non-deterministic functional programs language, fixpoint logic, theory of database operations. In this talk, from every non-trivial relational algebra R, we will construct via split idempotent construction an allegory such that a hom-set of the allegory is isomorphic to the R. The construction is comparable to Karoubi construction of ccc from a combinatory algebra. By proving the representation theorem of the allegories, we will represent R, too.
    6. 竹内 泉 (京大)
       Title: 二階型付計算による循環構造の解釈
       
  • 1/30 Session IV(15:45〜)
    7. 古森 雄一 (千葉大)
       Title: Category は Variety である
       Abstract: Category は Object と Arrow という２種類のものを含む部分代数系 (2 sorted partial algebraic system) であるが, Object を Identity Arrow と同一視し Arrow Only Category とみなせば普通の部分代数 系になる. 一般に部分代数において演算が定義されていない部分に 演算を定義して代数(total algebra)にできることは当たり前であるが, なるべく簡単な公理を満たすように演算を拡張することを考え次の 結果を得た. 与えられた Category の composition の定義を拡張して 等号だけで公理化できる代数系(variety)(Category algebra と名付ける) を作ることができる. 逆に作られた Category algebra から元の Category を取り出すこともできる.

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  問合せ先: sakurai@math.s.chiba-u.ac.jp (桜井貴文)