Mita Logic Seminar (Informal Meeting)
Paul-André Melliès博士講演会

日時： 2006年9月15日　16：00〜17：30

場所： 三田東宝ビル８F人文COE会議室 （＊場所等不明な方は慶大正門のガードマンにお尋ね下さい） (JR田町駅または都営地下鉄三田駅または赤羽橋駅（大江戸線）から 徒歩5分)
＊建物の入口が常時ロックされておりますので， ドア脇のインターホンにて7Fの事務室又は8Fをお呼び出し下さい．

講演者： Paul-André Melliès (Chargé de Recherches CNRS)

タイトル： Game semantics is a 2-dimensional Lawvere theory

アブストラクト： About six years ago, I worked with Peter Selinger on the categorical semantics of sequential games and polarized linear logic. We realized at the time that the two lifting operations L and R of game semantics:

-- L lifting an Opponent-starting game with an initial Player move,

-- R lifting a Player-starting game with an initial Opponent move

are adjoint functors, with L left adjoint to R.

In this talk, I will explain how to derive game semantics from the very existence of this adjunction. To that purpose, I will introduce the notion of 2-dimensional Lawvere theory, and show that arena games and innocent strategies define the 2-dimensional Lawvere theory of the particular kind of adjunction generated by a continuation model -- all this explained diagrammatically by string diagrams.

I will conclude my talk by discussing when such an adjunction generates a *-autonomous category, building on ideas by Masahito Hasegawa -- this providing a relevant "categorification" of Jean-Yves Girard's phase space model of linear logic.

問合せ先：
慶應義塾大学21世紀人文科学研究拠点
「心の統合的研究」センター　ワークショップ事務局
住所：東京都港区三田 3-1-7 三田東宝ビル 8F
e-mail：philosophy at abelard.flet.keio.ac.jp