Logic in Asia: Studia Logica Library

Editors-in-Chief Fenrong Liu, Tsinghua University and University of Amsterdam, Beijing, Hiroakira Ono, Advanced Institute of Science and Technology (JAIST), Ishikawa, Japan

Editorial Board Natasha Alechina, University of Nottingham, Nottingham, UK Toshiyasu Arai, Chiba University, Chiba Shi, Inage-ku, Japan Sergei Artemov, City University of New York, New York, NY, USA Mattias Baaz, Technical university of Vienna, Austria, Vietnam Lev Beklemishev, Institute of Russian Academy of Science, Russia Mihir Chakraborty, Jadavpur University, Kolkata, Phan Minh Dung, Asian Institute of Technology, Amitabha Gupta, Indian Institute of Technology Bombay, , India Christoph Harbsmeier, University of Oslo, Oslo, Norway Shier Ju, Sun Yat-sen University, Guangzhou, China Makoto Kanazawa, National Institute of Informatics, , Japan Fangzhen Lin, University of Science and Technology, Hong Kong Jacek Malinowski, Polish Academy of Sciences, Warsaw, Poland Ram Ramanujam, Institute of Mathematical Sciences, Chennai, India Jeremy Seligman, University of Auckland, Auckland, New Zealand Kaile Su, Peking University and Griffith University, Peking, China Johan van Benthem, University of Amsterdam and Stanford University, The Netherlands Hans van Ditmarsch, Laboratoire Lorrain de Recherche en Informatique et ses Applications, France Dag Westerstahl, Stockholm University, Stockholm, Sweden Yue Yang, National University, Singapore Syraya Chin-Mu Yang, National University, , China Logic in Asia: Studia Logica Library

This book series promotes the advance of scientific research within the field of logic in Asian countries. It strengthens the collaboration between researchers based in Asia with researchers across the international scientific community and offers a platform for presenting the results of their collaborations. One of the most prominent features of contemporary logic is its interdisciplinary character, combining mathematics, philosophy, modern computer science, and even the cognitive and social sciences. The aim of this book series is to provide a forum for current logic research, reflecting this trend in the field’s development. The series accepts books on any topic concerning logic in the broadest sense, i.e., books on contemporary formal logic, its applications and its relations to other disciplines. It accepts monographs and thematically coherent volumes addressing important developments in logic and presenting significant contributions to logical research. In addition, research works on the history of logical ideas, especially on the traditions in China and India, are welcome contributions. The scope of the book series includes but is not limited to the following:

• Monographs written by researchers in Asian countries. • Proceedings of conferences held in Asia, or edited by Asian researchers. • Anthologies edited by researchers in Asia. • Research works by scholars from other regions of the world, which fit the goal of “Logic in Asia”.

The series discourages the submission of manuscripts that contain reprints of previously published material and/or manuscripts that are less than 165 pages/ 90,000 words in length. Please also visit our webpage: http://tsinghualogic.net/logic-in-asia/background/

Relation with Studia Logica Library

This series is part of the Studia Logica Library, and is also connected to the journal Studia Logica. This connection does not imply any dependence on the Editorial Office of Studia Logica in terms of editorial operations, though the series maintains cooperative ties to the journal. This book series is also a sister series to Trends in Logic and Outstanding Contributions to Logic. For inquiries and to submit proposals, authors can contact the editors-in-chief Fenrong Liu at [email protected] or Hiroakira Ono at [email protected].

More information about this series at http://www.springer.com/series/13080 Beishui Liao • Thomas Ågotnes • Yi N. Wang Editors

Dynamics, Uncertainty and Reasoning The Second Chinese Conference on Logic and Argumentation

123 Editors Beishui Liao Thomas Ågotnes Center for the Study of Language University of Bergen and Cognition Bergen, Norway Zhejiang University, Xixi Campus Hangzhou, China

Yi N. Wang Zhejiang University Hangzhou, China

ISSN 2364-4613 ISSN 2364-4621 (electronic) Logic in Asia: Studia Logica Library ISBN 978-981-13-7790-7 ISBN 978-981-13-7791-4 (eBook) https://doi.org/10.1007/978-981-13-7791-4

© Springer Nature Singapore Pte Ltd. 2019 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Preface

Logic and argumentation are two highly related but somewhat different research areas. In our daily life, argumentation is ubiquitous, including not only deliberation and decision-making of individual agents, but also civil debate, dialogue, conver- sation and persuasion among a group of agents. It is about how conclusions or agreements can be reached through logical reasoning and/or dialogues. Unlike classical logics by which a set of inconsistent premises can lead to arbitrary and useless conclusions, (formal) argumentation can properly handle conflicting information, returning a set of conclusions satisfying some rational criteria. So, argumentation has a close relation to traditional non-monotonic logics and logic programming, such as default logic, circumscription, answer set programming, etc., where knowledge used for reasoning is allowed to be inconsistent. It has been shown that a number of non-monotonic logics and approaches of logic program- ming can be represented in argumentation. Besides inconsistency, another two important properties of the reasoning systems with incomplete information are uncertainty and dynamics. In recent years, different approaches have been proposed for combining argumentation and uncertainty, and for formulating dynamics of argumentation. This volume includes 6 papers selected from 16 submissions of the Second Chinese Conference on Logic and Argumentation (CLAR 2018) in 2018 held in Hangzhou, China, and 3 invited papers contributed by leading researchers in related fields. These papers nicely cover the fields of logic and argumentation, and the connection between them. On the one hand, from the perspective of argumentation, reasoning is realized by constructing, comparing and evaluating arguments. While the construction and comparison of arguments are studied in the direction of structured argumentation, which concerns how arguments and the relations over them are defined to satisfy some rationality postulates, the evaluation of the status of arguments is handled in an abstract argumentation framework (AF), which consists of a set of arguments and an attack relation over them. Among a set of conflicting arguments, a subset of collectively accepted arguments is called an extension, and a function mapping an AF to a set of extensions is called an (extension-based) argumentation semantics.

v vi Preface

In terms of different evaluating criteria, there are different argumentation semantics, including complete, grounded, preferred, stable, naive, etc. Although argumentation semantics have been extensively studied in the argu- mentation community, there are still some interesting research problems, especially the ones related to uncertainty and dynamics. In this volume, Yuming Xu, Lidong Xu and Claudette Cayrol provide a structural analysis of extension-based argu- mentation semantics, based on a notion of joint acceptability. They show that using this new approach, an admissible set, a complete extension, or a preferred extension can be iteratively built from a conflict-free collection of initial sets. Jérémie Dauphin, Marcos Cramer and Leendert van der Torre introduce a dynamic approach for combining argumentation semantics. They show that the merging of preferred semantics and grounded semantics is complete semantics, and that fea- tures of naive-based and complete-based semantics can be meaningfully combined. Stefano Bistarelli, Francesco Santini and Carlo Taticchi study the dynamics of argumentation by introducing local-expansion invariant operators in argumentation semantics, such that for conflict-free sets or admissible sets of arguments in an AF, applying such operators to the AF does not produce any change to the sets. Kang Xu, Beishui Liao and Huaxin Huang present an approach to update an AF such that a given set of arguments can be enforced to be an extension of the AF, by defining general rules. This approach is based on a notion of characterizing an AF with respect to a given set of arguments. On the other hand, from the perspectives of logic and the interplay of logic and argumentation, in addition to trying to understand the various logics themselves, it is interesting to investigate how various logics can be represented by argumenta- tion, and how some aspects (e.g. semantics and computation) of argumentation can be formulated by logics. Along these lines, in this volume, Huimin Dong, Norbert Gratzl and Olivier Roy propose a new solution to the well-known Free Choice Permission Paradoxes, by combining ideas from substructural logics and non-monotonic reasoning. Jie Fan introduces a uniform method for constructing ultrafilter extensions from canonical models, based on the similarity between ultrafilters and maximal consistent sets. Mengyuan Zhao develops game-theoretic models as a unified account for both implicatures and soft presuppositions, and explains why soft presuppositions project non-uniformly through different types of quantifiers, and why soft presuppositions are easily defeasible. It is interesting to note that although these three papers do not directly focus on the connections between various logics and argumentation, they share some important aspects with argumentation, including utilizing principles of non-monotonic reasoning, defining maximal consistent sets and handling defeasibility of reasoning. Besides these three papers, the remaining two papers are exactly in the direction of connecting logic and argumentation. Sylvie Doutre, Andreas Herzig and Laurent Perrussel study abstract argumentation in dynamic logic, by encoding AFs and their dynamics in Dynamic Logic of Propositional Assignments (DL-PA). David Fuenmayor and Christoph Benzmüller utilize higher order automated deduction technologies for the logical analysis of natural language arguments. Preface vii

We would like to thank all the authors who submitted contributions, the invited speakers (Natasha Alechina, Anthony Hunter, Xudong Luo and Tjitze Rienstra), as well as the program committee of CLAR 2018 (Pietro Baroni, Stefano Bistarelli, Alexander Bochman, Dragan Doder, Shanshan Du, Massimiliano Giacomin, Jiahong Guo, Andreas Herzig, Fengkui Ju, Fenrong Liu, Hu Liu, Minghui Ma, Nir Oren, Olivier Roy, Katsuhiko Sano, Guillermo Simari, Christian Straßer, Matthias Thimm, Hans van Ditmarsch, Leon van der Torre, Serena Villata, Stefan Woltran, Yun Xie, Fan Yang and Junhua Yu). We thank local organizers (Huimin Dong, Fanghong Shi and Teng Ying) for their excellent work, and Zhe Yu for her help in the process of editing this volume. Meanwhile, we are grateful to Fenrong Liu and Hiroakira Ono, the editor in chief of this book series ‘Logic in Asia’ (LIAA), for their supportive recommen- dation of this volume to LIAA, and to Fiona Wu and Leana Li, for their support in the process of publication of this volume. Finally, we acknowledge that CLAR 2018 is financially supported by the Fundamental Research Funds for the Central Universities of China for the project Big Data, Reasoning and Decision Making.

Hangzhou, China Beishui Liao [email protected] Bergen, Norway Thomas Ågotnes Hangzhou, China Yi N. Wang January 2019 Contents

Structural Analysis of Extension-Based Argumentation Semantics with Joint Acceptability ...... 1 Yuming Xu, Lidong Xu and Claudette Cayrol A Dynamic Approach for Combining Abstract Argumentation Semantics ...... 21 Jérémie Dauphin, Marcos Cramer and Leendert van der Torre Local Expansion Invariant Operators in Argumentation Semantics .... 45 Stefano Bistarelli, Francesco Santini and Carlo Taticchi Updating Argumentation Frameworks for Enforcing Extensions ...... 63 Kang Xu, Beishui Liao and Huaxin Huang Open Reading and Free Choice Permission: A Perspective in Substructural Logics ...... 81 Huimin Dong, Norbert Gratzl and Olivier Roy A Road to Ultrafilter Extensions ...... 117 Jie Fan Soft Presuppositions as Scalar Implicatures in Signaling Games ...... 135 Mengyuan Zhao Abstract Argumentation in Dynamic Logic: Representation, Reasoning and Change ...... 153 Sylvie Doutre, Andreas Herzig and Laurent Perrussel Computational Hermeneutics: An Integrated Approach for the Logical Analysis of Natural-Language Arguments ...... 187 David Fuenmayor and Christoph Benzmüller

ix Contributors

Christoph Benzmüller Freie Universität Berlin, Berlin, Germany; University of Luxembourg, Esch-sur-Alzette, Luxembourg Stefano Bistarelli Università degli Studi di, Perugia, Italy Claudette Cayrol IRIT, Universite de Toulouse, CNRS, Toulouse, France Marcos Cramer TU Dresden, Dresden, Germany Jérémie Dauphin University of Luxembourg, Luxembourg, Luxembourg Huimin Dong Department of Philosophy, Zhejiang University, Hangzhou, China Sylvie Doutre IRIT, Université Toulouse 1 Capitole, Toulouse, France Jie Fan School of Humanities, University of Chinese Academy of Sciences, Beijing, China David Fuenmayor Freie Universität Berlin, Berlin, Germany Norbert Gratzl MCMP, LMU Munich, Munich, Germany Andreas Herzig IRIT, CNRS, Toulouse, France Huaxin Huang Center for the Study of Language and Cognition, Zhejiang University, Hangzhou, China Beishui Liao Center for the Study of Language and Cognition, Zhejiang University, Hangzhou, China Laurent Perrussel IRIT, Université Toulouse 1 Capitole, Toulouse, France Olivier Roy Institut für Philosophie, Universität Bayreuth, Bayreuth, Germany Francesco Santini Università degli Studi di, Perugia, Italy Carlo Taticchi Gran Sasso Science Institute, L’Aquila, Italy

xi xii Contributors

Leendert van der Torre University of Luxembourg, Luxembourg, Luxembourg Kang Xu Zhejiang University of Water Resources and Electric Power, Hangzhou, China Lidong Xu School of Mathematics, Shandong University, Jinan, China Yuming Xu School of Mathematics, Shandong University, Jinan, China Mengyuan Zhao School of Marxism, University of Shanghai for Science and Technology, Shanghai, China