Outstanding Contributions to Logic 8 Katalin Bimbó Editor J. Michael Dunn on Information Based Logics Outstanding Contributions to Logic Volume 8 Editor-in-chief Sven Ove Hansson, Royal Institute of Technology, Stockholm, Sweden Editorial Board Marcus Kracht, Universität Bielefeld Lawrence Moss, Indiana University Sonja Smets, Universiteit van Amsterdam Heinrich Wansing, Ruhr-Universität Bochum More information about this series at http://www.springer.com/series/10033 Katalin Bimbó Editor J. Michael Dunn on Information Based Logics 123 Editor Katalin Bimbó Department of Philosophy University of Alberta Edmonton, AB Canada ISSN 2211-2758 ISSN 2211-2766 (electronic) Outstanding Contributions to Logic ISBN 978-3-319-29298-4 ISBN 978-3-319-29300-4 (eBook) DOI 10.1007/978-3-319-29300-4 Library of Congress Control Number: 2016930054 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by SpringerNature The registered company is Springer International Publishing AG Switzerland To J. Michael Dunn on (or near) his 75th birthday Preface An obvious excuse for the project that resulted in the present collection of papers is provided by the dedication: J. Michael Dunn turns 75 years old in 2016. This book celebrates his research and his career as a logician, which already spans more than half a century. Another obvious rationale for this book is that we are aware, more than ever before, of the importance and pervasiveness of information. It is a truism that we live in an information age. The developments in computer technology in the past 20–30 years—including increased storage, transmission, and search capabilities— undoubtedly contribute to our perception of the ubiquity of information. A way to use information is to reason with it. Remarkably, J. M. Dunn was thinking about logic in terms of information well before everybody jumped onto the (i-)bandwagon wheeling along the information superhighway. The papers in this volume evidence that treating logic as an organon for manipulating information is a fruitful approach. An opportunity to assemble this volume arose because Springer established a new book series. The Outstanding Contributions to Logic series provides a different focal point for a collection of papers than some others do. Although the OCL volumes have the flavor of a Festschrift, they support greater flexibility and a narrower theme than what could be achieved by cataloging all the works of a famous logician. Logic, in general, should interest a wide range of people. The particular approach to logic that is exemplified by this volume will primarily appeal to readers who are involved with disciplines such as mathematics, computer science, the information sciences, and philosophy. Some of the papers include not only new research results, but draw a chronologically faithful picture of the development of certain ideas—these sources will be especially useful for historians of science and philosophers. A reflection on achievements (spanning several decades) motivated some authors to take stock of the accumulated results; such papers are excellent for reference purposes too. It is expected that the present book will be useful to scholars who are interested in the area that is somewhat vaguely called nonclassical logics. While the papers vii viii Preface will definitely be invaluable for researchers, most of them should be accessible to graduate students as well as to researchers working in other fields. Some articles in this collection are written in a style which ensures that anyone who is willing to dabble into a subject (outside their expertise) will enjoy reading them. Acknowledgments. In a volume of this kind, the person whose work and research results provide the justification for editing the volume is to be thanked first: I am grateful to J. Michael Dunn for allowing me to take on the (somewhat complicated) task of editing this volume and for his continuous help in making the project a success. I would like to thank the authors of this volume, who not only responded to the initial invitation to contribute to this volume, but have written a paper for this collection. The papers were refereed using the “single-blind” type of refereeing. Thanks to those who refereed a paper, and thereby, contributed to the project. The series editor, Sven Ove Hansson not only provided a document about how to edit a book for the Outstanding Contributions to Logic series, but he was helpful in various other ways from start to finish. I am grateful for his help in the process. Christi Lue of Springer Science provided forms, guidelines, and advice from the publisher’s side. I am thankful for her ongoing support to the project. This book has been typeset using the program TEX (which was originally designed by D. Knuth) from the source files submitted by the authors. In particular, the volume uses the LATEX format, a class file provided by Springer as well as several packages that were developed under the auspices of the American Mathematical Society. Edmonton Katalin Bimbó September 2015 Contents An Engineer in Philosopher’s Clothing . xvii J. Michael Dunn J. Michael Dunn’s Publications . xxxv Introduction: From Information at Large to Semantics of Logics ..... 1 Katalin Bimbó RM and its Nice Properties ................................. 15 Arnon Avron Wedge Sum, Merge and Inconsistency ......................... 45 Chris Mortensen Single Axioms and Axiom-Pairs for the Implicational Fragments of R, R-Mingle, and Some Related Systems ..................... 53 Dolph Ulrich LC and Its Pretabular Relatives ............................. 81 Larisa Maksimova The Story of γ........................................... 93 Alasdair Urquhart Manipulating Sources of Information: Towards an Interpretation of Linear Logic and Strong Relevance Logic .................... 107 Edwin Mares Epistemic Relevance and Epistemic Actions ..................... 133 Sebastian Sequoiah-Grayson Comparing Contents with Information......................... 147 Ross T. Brady ix x Contents On Split Negation, Strong Negation, Information, Falsification, and Verification ......................................... 161 Heinrich Wansing Truth, Falsehood, Information and Beyond: The American Plan Generalized......................................... 191 Yaroslav Shramko Logical Foundations of Evidential Reasoning with Contradictory Information.............................. 213 Chunlai Zhou Probabilistic Interpretations of Predicates ...................... 247 Janusz Czelakowski Reasoning with Incomplete Information in Generalized Galois Logics Without Distribution: The Case of Negation and Modal Operators .............................................. 279 Chrysafis Hartonas Mereocompactness and Duality for Mereotopological Spaces......... 313 Robert Goldblatt and Matt Grice Distributed Modal Logic ................................... 331 Gerard Allwein and William L. Harrison Tracking Information ..................................... 363 Johan van Benthem Syllogistic Logic with Cardinality Comparisons .................. 391 Lawrence S. Moss A “Reply” to My “Critics” ................................. 417 J. Michael Dunn Index ................................................. 435 Editor and Contributors About the Editor Katalin Bimbó is a professor at the University of Alberta, in Edmonton, Canada. Her main research interests and results are in the areas of relevance logic (espe- cially, ticket entailment), substructural logics (including linear logic) and combi- natory logic and λ-calculi. She received her Ph.D. from Indiana University Bloomington (with J. M. Dunn as her thesis supervisor), and then worked at uni- versities in New Zealand, Australia and the U.S.A. She is an author of numerous journal articles and book chapters. She co-authored a book with J. M. Dunn, entitled Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi (2008), and she wrote two more books, Combinatory Logic: Pure, Applied and Typed (2012) and Proof Theory: Sequent Calculi and Related Formalisms (2015). Contributors Gerard Allwein received his BS in Computer Science from Purdue University in 1979, and his Ph.D. from Indiana University in 1992 with J. Michael Dunn as his advisor. He spent several years as an engineer in the machine tools industry. He is the former Assistant Director of the Visual Inference Laboratory at Indiana University and has taught the