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.

「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
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