Preface

The 35th MLG meeting was held at Echigo-Yuzawa, Japan on January 9– 11, 2002. The meeting was supported mainly by Grant-in-Aid for Scientific Research (C)(2) No. 13640109, Substructural Logics and Algebraic Structures, whose head investigator is Hiroakira Ono, Japan Advanced Institute of Science and Technology, Hokuriku, and Grant-in-Aid for Scientific Research on Priority Areas Research (C) No. 13224052, Theoretical Study on New Softwares with Dynamic Binding Mechanism of Variables, whose head investigator is Masahiko Sato, Kyoto University, Kyoto.

There were 32 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 20, 2002

Table of Contents

λρ-Calculus: A Natural Deduction for Classical Logic 1 Yuichi Komori

Quantum machanics and Quantum logic 4 Haruhiko Kozawa

Representation of quantum proposition in quantale valued universe 7 Satoko Titani

Completions of a metric space without choice 10 Masahiko Murakami

Representation of preference orders by hyperreal numbers 12 Kiyoshi Ikeda

Kripke incompleteness of predicate extensions of Gabbay de Jongh’s logic

of finite binary trees 15 Tatsuya Shimura

Products of infinitely many modal logics 18 Yasusi Hasimoto

Proof Theoretical Studies on Semilattice Relevant Logics 21 Ryo Kashima

Learning word-to-meaning mappings in logical semantics 24 Makoto Kanazawa

Some properties on orthologics 27 Yutaka Miyazaki

Tableau System and Theorem Prover for Temporal Logic Kt 30 Akio Maruyama and Toshimasa Matsumoto

A Sahlqvist theorem for relevant modal logics 33 Takahiro Seki

An Efficient Construction of Counter-Models for Modal Logic K4 36 Motohiko Mouri

On complementary modalities 39 Yuko Murakami

A Map of Common Knowledge Logics 41 Nobu-Yuki Suzuki On Bimodal Provability Logics 44

Katsumi Sasaki

Elementary ordinal representation systems for KP theories 47 Osamu Takaki

Groups in Allegories 50 Yasuo Kawahara

A remark on canonicity 53 Tomasz Kowalski

Games on Finite Graphs and Temporal Logic 56 Bakhadyr M. Khoussainov

Standard completeness of predicate logic MTL∀ for left-continuous t-norms 59 Hiroakira Ono iv