Preface

The 34th MLG meeting was held at Echigo-Yuzawa, Japan on January 9– 12, 2001. The meeting was supported mainly by Grant-in-Aid for Scientific Research (B)(1) No. 10440027, Advances in Nonclassical Logic and for Exploratory Research No. 11874016, Algebra for Substructural Logics, both of whose head investigator is Hiroakira Ono, Japan Advanced Institute of Science and Technology, Hokuriku.

There were 24 participants. This volume contains extended abstracts of the talks presented at the meeting.

We are extremely grateful to all the speakers and participants who made this meeting successful. We hope this volume will contribute to the further progress of mathematical logic and its related area.

Yuichi KOMORI Takafumi SAKURAI January 18, 2001

Talbe of Contents

The curse of constructive mathematics

-Can the gadget computer go beyond the NP problem?- 1 Eido Kyuma

Models for Modal Logics over KR 5 Takahiro Seki

Subframe logics for S4-type intuitionistic modal logic 10 Kazuyo Inoi

Residuation Theory and Substructural Logics 15 Hiroakira Ono

Alternatives to the relevant logic R 19 Ryo Kashima

A Kripke Type Semantics for Substructural Logics with Strong Negation 23 Norihiro Kamide

Kripke completeness of predicate extensions of cofinal subframe logics 25 Tatsuya Shimura

On Komori Algebras 30 Yuichi Komori

An Extension of Martin-Löf’s Type Theory with an Evolution Relation 33 Tadao Ishii

Fuzzy relations and fuzzy mappings between fuzzy subsets 38 Mamoru Shimoda

Theorem Provers with Counter Models from xpe 43 Motohiko Mouri

Initial segments of Rudin-Frolík order 48 Masahiko Murakami

Atomic incompleteness 53 Marcus Kracht and Tomasz Kowalski

On Quantales 55 Haruhiko Kozawa

Quantale valued set theory 60 Satoko Titani