京都大学の五十嵐です．
来たる4/11(金)に University of Warsaw の Andrzej Tarlecki さんをお迎え して，以下の要領でセミナーを行う予定です．
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よろしくお願いいたします．
日時: 4/11(金) 13:30〜14:30 場所: 京都大学吉田キャンパス総合研究7号館(旧工学部10号館) 1階 セミナー室1
==================================================================== Categories, Institutions, Abstract Model Theory, and Software Specification
Andrzej Tarlecki University of Warsaw
One goal of this presentation is to show some examples where the use of category theory, via the theory of institutions, led to beautiful, general and generic results, applicable in many different contexts, and to a better understanding of some standard classical results and ideas from mathematical logic and from the theory of algebraic specifications.
The theory of institutions uses the language of category theory to offer a simple formalisation of the concept of a logical system, where sentences and semantic structures are abstract objects linked by a satisfaction relation, classified by (abstract) signatures. The key tool used when working with institutions is a categorical structure imposed on the collection of signatures, together with (covariant) translations of sentences and (contravariant) reducts of semantic structures induced by signature morphisms in a way that preserves satisfaction. Nearly all (if not quite all) logical systems fit such an institutional mould. An ambitious research programme is to mimic developments that classically concern, or rely on a particular logical system within an arbitrary institution, perhaps subject to some further requirements. In this way, we may arrive at general results that apply to many logical systems and, perhaps more importantly, capture a better understanding of the essence of many classical results and ideas.
In this talk I will present the basics of the theory of institutions, and will draw examples from institutional abstract model theory (interpolation and definability results) and foundations of software specification and development (specification structure and its use) to illustrate this point. -- 五十嵐 淳 (IGARASHI Atsushi) E-mail: igarashi@kuis.kyoto-u.ac.jp url: http://www.fos.kuis.kyoto-u.ac.jp/~igarashi/