[logic-ml] Talk by Keiko Nakata (Tallinn University of Technology), Tue 18 December 2012

[Ichiro Hasuo]

みなさま，

東京大学の蓮尾と申します．
来る12月18日，タリン工科大学の中田景子さんをお迎えしてご講演いただきます．
（2題，連続講演です）

詳細は以下です．ご興味のある方はぜひお越しください！

蓮尾 一郎
http://www-mmm.is.s.u-tokyo.ac.jp/

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Tue 18 December 2012, 16:40-18:10
Keiko Nakata (Tallinn University of Technology), 2 titles
理学部7号館1階 102教室   Room 102, School of Science Bldg. No. 7

Title
Proving open induction using delimited control operators

Abstract
Open Induction (OI) is a principle classically equivalent to Dependent
Choice, which is, unlike the later, closed under double-negation
translation and A-translation. In the context of Constructive Reverse
Mathematics, Wim Veldman has shown that, in presence of Markov's
Principle, OI on Cantor space is equivalent to Double-negation Shift
(DNS). With Danko Ilik, we have reworked Veldman's proof to give a
constructive proof of OI, where DNS is interpreted using delimited
control operators.

Joint work with Danko Ilik.

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Title
Walking through infinite trees with mixed induction and coinduction:
A Proof Pearl with the Fan Theorem and Bar Induction.

Abstract
We study temporal properties over infinite binary red-blue trees in
the setting of constructive type theory. We consider several familiar
path-based properties, typical to linear-time and branching-time
temporal logics like LTL and CTL*, and the corresponding tree-based
properties, in the spirit of the modal mu-calculus. We conduct a
systematic study of the relationships of the path-based and tree-based
versions of ``eventually always blueness '' and mixed
inductive-coinductive ``almost always blueness'' and arrive at a
diagram relating these properties to each other in terms of
implications that hold either unconditionally or under specific
assumptions (Weak Continuity for Numbers, the Fan Theorem, Lesser
Principle of Omniscience, Bar Induction).

Joint work with Marc Bezem and Tarmo Uustalu.