Trends in Logic Volume 55
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Trends in Logic Volume 55
TRENDS IN LOGIC
Studia Logica Library
VOLUME 55
Editor-in-Chief
Heinrich Wansing, Department of Philosophy, Ruhr University Bochum,
Bochum, Germany
Editorial Board
Arnon Avron, Department of Computer Science, University of Tel Aviv, Tel Aviv, Israel
Katalin Bimbó, Department of Philosophy, University of Alberta, Edmonton, AB, Canada
Giovanna Corsi, Department of Philosophy, University of Bologna, Bologna, Italy
Janusz Czelakowski, Institute of Mathematics and Informatics, University of Opole,
Opole, Poland
Roberto Giuntini, Department of Philosophy, University of Cagliari, Cagliari, Italy
Rajeev Goré, Australian National University, Canberra, ACT, Australia
Andreas Herzig, IRIT, University of Toulouse, Toulouse, France
Wesley Holliday, UC Berkeley, Lafayette, CA, USA
Andrzej Indrzejczak, Department of Logic, University of Lódz, Lódz, Poland
Daniele Mundici, Mathematics and Computer Science, University of Florence, Firenze, Italy
Sergei Odintsov, Sobolev Institute of Mathematics, Novosibirsk, Russia
Ewa Orlowska, Institute of Telecommunications, Warsaw, Poland
Peter Schroeder-Heister, Wilhelm-Schickard-Institut, Universität Tübingen, Tübingen,
Baden-Württemberg, Germany
Yde Venema, ILLC, Universiteit van Amsterdam,
Amsterdam, Noord-Holland, The Netherlands
Andreas Weiermann, Vakgroep Zuivere Wiskunde en Computeralgebra, University of Ghent,
Ghent, Belgium
Frank Wolter, Department of Computing, University of Liverpool, Liverpool, UK
Ming Xu, Department of Philosophy, Wuhan University, Wuhan, China
Jacek Malinowski, Institute of Philosophy and Sociology, Polish Academy of Sciences,
Warszawa, Poland
Assistant Editor
Daniel Skurt, Ruhr-University Bochum, Bochum, Germany
Founding Editor
Ryszard Wojcicki, Institute of Philosophy and Sociology, Polish Academy of Sciences,
Warsaw, Poland
The book series Trends in Logic covers essentially the same areas as the journal Studia Logica, that is,
contemporary formal logic and its applications and relations to other disciplines. The series aims at publishing
monographs and thematically coherent volumes dealing with important developments in logic and presenting
significant contributions to logical research.
Volumes of Trends in Logic may range from highly focused studies to presentations that make a subject
accessible to a broader scientific community or offer new perspectives for research. The series is open to
contributions devoted to topics ranging from algebraic logic, model theory, proof theory, philosophical logic,
non-classical logic, and logic in computer science to mathematical linguistics and formal epistemology. This
thematic spectrum is also reflected in the editorial board of Trends in Logic. Volumes may be devoted to
specific logical systems, particular methods and techniques, fundamental concepts, challenging open problems,
different approaches to logical consequence, combinations of logics, classes of algebras or other structures, or
interconnections between various logic-related domains. Authors interested in proposing a completed book or a
manuscript in progress or in conception can contact either christi.lue@springer.com or one of the Editors of the
Series.
More information about this series at http://www.springer.com/series/6645Davide Fazio Antonio Ledda
• •
Francesco Paoli
Editors
Algebraic Perspectives
on Substructural Logics
123Editors Davide Fazio Antonio Ledda Dipartimento di Pedagogia Dipartimento di Pedagogia Psicologia, Filosofia Psicologia, Filosofia Università di Cagliari Università di Cagliari Via Is Mirrionis, Cagliari, Italy Via Is Mirrionis, Cagliari, Italy Francesco Paoli Dipartimento di Pedagogia Psicologia, Filosofia Università di Cagliari Via Is Mirrionis, Cagliari, Italy ISSN 1572-6126 ISSN 2212-7313 (electronic) Trends in Logic ISBN 978-3-030-52162-2 ISBN 978-3-030-52163-9 (eBook) https://doi.org/10.1007/978-3-030-52163-9 © Springer Nature Switzerland AG 2021 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Acknowledgements
The editors gratefully acknowledge the following funding sources: Project “Per un’
estensione semantica della Logica Computazionale Quantistica—Impatto teorico e
ricadute implementative”, Regione Autonoma della Sardegna, (RAS: RASSR40341),
L.R. 7/2017, annualità 2017—Fondo di Sviluppo e Coesione (FSC) 2014–2020;
MIUR, within the projects PRIN 2017: “Logic and cognition. Theory, experiments,
and applications”, CUP: 2013YP4N3, and PRIN 2017: “Theory and applications of
resource sensitive logics”, CUP: 20173WKCM5 and gratefully acknowledge the
support of the Horizon 2020 program of the European Commission: SYSMICS
project, number: 689176, MSCA-RISE-2015. Finally, we thank the community of
researchers in the area of substructural logics and residuated structures, in particular
Hiroakira Ono and Constantine Tsinakis who played a decisive role in creating it and
in fostering the mutual collaboration among its members.
vContents
Editorial Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Davide Fazio, Antonio Ledda, and Francesco Paoli
Distributivity and Varlet Distributivity . . . . . . . . . . . . . . . . . . . . . . . . . 11
Paolo Aglianò
On Distributive Join Semilattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Rodolfo C. Ertola-Biraben, Francesc Esteva, and Lluís Godo
Implication in Weakly and Dually Weakly Orthomodular Lattices . . . . 41
Ivan Chajda and Helmut Länger
Residuated Operators and Dedekind–MacNeille Completion . . . . . . . . . 57
Ivan Chajda, Helmut Länger, and Jan Paseka
PBZ*–Lattices: Ordinal and Horizontal Sums . . . . . . . . . . . . . . . . . . . . 73
Roberto Giuntini, Claudia Mureşan, and Francesco Paoli
EMV-Algebras—Extended MV-Algebras . . . . . . . . . . . . . . . . . . . . . . . . 107
Anatolij Dvurečenskij and Omid Zahiri
Quasi-Nelson; Or, Non-involutive Nelson Algebras . . . . . . . . . . . . . . . . 133
Umberto Rivieccio and Matthew Spinks
Hyperdoctrines and the Ontology of Stratified Semantics . . . . . . . . . . . 169
Shay Allen Logan
viiContributors
Paolo Aglianò DIISM, University of Siena, Siena, Italy
Ivan Chajda Faculty of Science, Department of Algebra and Geometry, Palacký
University Olomouc, Olomouc, Czech Republic
Anatolij Dvurečenskij Mathematical Institute, Slovak Academy of Sciences,
Bratislava, Slovakia; Faculty of Sciences, Palacký University Olomouc, Olomouc,
Czech Republic
Rodolfo C. Ertola-Biraben CLE-UNICAMP, Campinas, SP, Brazil
Francesc Esteva IIIA-CSIC, Belaterra, Spain
Antonio Ledda Dipartimento di Pedagogia, Psicologia, Filosofia, Università di
Cagliari, Cagliari, Italy
Francesco Paoli Dipartimento di Pedagogia, Psicologia, Filosofia, Università di
Cagliari, Cagliari, Italy
Davide Fazio Dipartimento di Pedagogia, Psicologia, Filosofia, Università di
Cagliari, Cagliari, Italy
Roberto Giuntini Dipartimento di Pedagogia, Psicologia, Filosofia, Università di
Cagliari, Cagliari, Italy
Lluís Godo IIIA-CSIC, Belaterra, Spain
Helmut Länger Institute of Discrete Mathematics and Geometry TU Wien
Wiedner Hauptstraße 8-10 1040 Vienna Austria and Department of Algebra and
Geometry, Palacký University Olomouc 17., Olomouc, Czech Republic
Shay Allen Logan Kansas State University, Manhattan, KS, USA
Claudia Mureşan Dipartimento di Pedagogia, Psicologia, Filosofia, Università di
Cagliari, Cagliari, Italy
ixx Contributors Jan Paseka Faculty of Science, Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic Umberto Rivieccio Departamento de Informática e Matemática Aplicada, Universidade Federal do Rio Grande do Norte, Natal, Brazil Matthew Spinks Dipartimento di Pedagogia, Psicologia, Filosofia, Università di Cagliari, Cagliari, Italy Omid Zahiri University of Applied Science and Technology, Tehran, Iran
You can also read
