Logic and Argumentation: 4th International Conference, CLAR 2021, Hangzhou, China, October 20–22, 2021, Proceedings

Preface
Organization
On the Need of Knowledge for Computational Argument Analysis and Generation (Abstract of Invited Talk)
Contents
Invited Papers
Resolving the Cohenian Paradox in Judicial Probability Theory
	1 Introduction
	2 The Selection Problem: Subjective vs Objective Probability
	3 The Calculation Problem: A Franklinian Solution
	4 The Conjunction Problem: A Probabilistic Justification
	5 Conclusion
	References
Focusing the Argumentative Process: Neighborhood-Based Semantics in Abstract Argumentation
	1 Introduction
	2 Background
		2.1 Hashtagged Argumentation Framework
		2.2 Proximity-Based Semantics
	3 Argument Neighborhoods: A Topological View
	4 Neighborhood-Bounded Admissibility
	5 Related Work and Conclusions
	References
Burdens of Persuasion and Standards of Proof in Structured Argumentation
	1 Introduction
	2 Burdens of Production and Burdens of Persuasion
	3 Argumentation Framework
		3.1 Defeasible Theories
		3.2 Defeat with Burdens of Persuasion
		3.3 Example
	4 A Labelling Semantic for Burdens of Persuasion
		4.1 Argumentation Graphs and Bp-Labelling
		4.2 Examples
		4.3 The Problem of Defeat Cycles
	5 Adversarial Burden of Persuasion
	6 Standards of Proof
		6.1 From Priorities to Bandwidths
		6.2 Examples
	7 Conclusion
	References
Implementation of Choice of Jurisdiction and Law in Private International Law by PROLEG Meta-interpreter
	1 Introduction
	2 Reasoning About Jurisdiction
		2.1 Syntax of Modular-PROLEG
		2.2 Modular-PROLEG Semantics a la Answer Set Programming
		2.3 Meta Interpreter of Modular-PROLEG
		2.4 Example of Reasoning About Jurisdiction
	3 Reasoning About Choice of Law
		3.1 Syntax of Modular-PROLEG for PIL
		3.2 Semantics for Modular-PROLEG for PIL
		3.3 Meta-interpreter of Modular-PROLEG for PIL
		3.4 Example of Reasoning About International Affairs
	4 Conclusion
	References
Full Papers
Collective Argumentation with Topological Restrictions
	1 Introduction
	2 Argumentation Framework and Topological Property
	3 The Aggregation Model
	4 Topological Restriction
	5 Preservation Results with Topological Restrictions
		5.1 Acyclicity
		5.2 Symmetry
	6 The Majority Rule and Topological Restrictions
	7 Conclusion
	References
The Choice-Preferred Semantics for Relevance-Oriented Acceptance of Admissible Sets of Arguments
	1 Introduction
	2 Preliminaries
	3 A Novel Principle: SAFWOC
	4 Motivation for New Semantics
	5 Choice-Preferred Semantics
	6 Satisfaction of Principles
	7 Conclusion and Future Work
	References
New Weak Admissibility Semantics for Abstract Argumentation
	1 Introduction
	2 Preliminaries
	3 New Weak Admissibility Semantics
	4 Principles
	5 Related and Future Work
	6 Conclusion
	References
On Restricting the Impact of Self-attacking Arguments in Gradual Semantics
	1 Introduction
	2 Formal Setting and Existing Semantics
		2.1 h-categorizer Semantics
		2.2 M&T Semantics
	3 Principles for Gradual Semantics
	4 Analysis of Principles and Links Between Them
	5 No Self-Attack h-categorizer Semantics
	6 Principle-Based Evaluation of Semantics
	7 Experimental Results
	8 Summary
	References
Flexible Dispute Derivations with Forward and Backward Arguments for Assumption-Based Argumentation
	1 Introduction
	2 Formal Background
	3 Argument-Based Flexible Dispute Derivations
		3.1 Argument and Dispute State Expansions
		3.2 Argument-Based Flexible Dispute Derivations Following Structured and Graph-Based Dispute Derivations
		3.3 Flexible Dispute Derivations
	4 Rule-Based Flexible Dispute Derivations
	5 Implementation
	6 Conclusions and Future Work
	References
Towards a General Theory of Decomposability in Abstract Argumentation
	1 Introduction
	2 Background
	3 A General Model for Decomposability
		3.1 Modelling Local Information
		3.2 The Notions of Local Function and Decomposability
	4 On the Power of Local Information Functions
	5 The Canonical Local Function
	6 Discussion and Conclusion
	References
Abstract Argumentation with Qualitative Uncertainty: An Analysis in Dynamic Logic
	1 Introduction
	2 Background
		2.1 Abstract Argumentation Frameworks and Their Stable Semantics
		2.2 Dynamic Logic of Propositional Assignments (DL-PA)
	3 Formalisms for Arguing with Qualitative Uncertainty
	4 Incomplete AFs in DL-PA
	5 Rich Incomplete AFs in DL-PA
	6 Control AFs in DL-PA
	7 Constrained Incomplete AFs and Their Encoding in DL-PA
	8 Discussion and Future Work
	References
Explanations of Non-monotonic Inference in Admissibility-Based Abstract Argumentation
	1 Introduction
	2 Preliminaries
	3 Explainability Framework
	4 Implementation
	5 Discussion
	6 Conclusion
	References
The Burden of Persuasion in Abstract Argumentation
	1 Introduction
	2 Preliminaries
	3 An Abstract Argumentation-Based Burden of Persuasion
	4 Semantics Selection and Skeptical Acceptance
	5 Discussion
	6 Conclusion
	References
Handling Support Cycles and Collective Interactions in the Logical Encoding of Higher-Order Bipolar Argumentation Frameworks
	1 Introduction
	2 Background on REBAF Given in ch14CFFLS18bspssh
	3 Background on the Logical Description of a REBAF Given in ch14CLS20
	4 REBAF with Support Cycles: Analysis and New Proposition
	5 Collective Interactions in REBAF: Impact on the Logical Encoding
	6 Conclusion and Future Works
	A Sketchs of Proof
	References
Tableau-Based Decision Procedure for Logic of Knowing-How via Simple Plans
	1 Introduction
	2 Preliminaries
	3 Tableau System for ELKh
	4 Completeness
	5 Decision Procedure
	6 Conclusion
	References
Integrating Individual Preferences into Collective Argumentation
	1 Introduction
	2 Preliminaries
	3 A Novel Method for Framework Merging
	4 Incomplete Preference Aggregation
	5 The Concordance Between Collective Framework and Social Preference
	6 Conclusion
		6.1 Related Work
		6.2 Future Work
	References
A Logic for Binary Classifiers and Their Explanation
	1 Introduction
	2 A Language for Binary Classifiers
		2.1 Basic Language and Classifier Model
		2.2 Properties of Classifier Models
	3 Counterfactual Conditional
	4 Explanations and Biases
		4.1 Prime Implicant Expressed in CM
		4.2 Abductive Explanation (AXp)
		4.3 Contrastive Explanation (CXp)
		4.4 Decision Bias
	5 Axiomatization and Complexity
	6 Extensions
		6.1 Dynamic Extension
		6.2 Epistemic Extension
	7 Conclusion
	References
Extension-Based Semantics for Incomplete Argumentation Frameworks
	1 Introduction
	2 Background
		2.1 Abstract Argumentation Frameworks
		2.2 Qualitative Uncertainty in AFs
	3 Generalizing Extension-Based Semantics from PAFs to IAFs
		3.1 Conflict-Free and Admissible Sets of IAFs
		3.2 Admissibility-Based Semantics for IAFs
		3.3 Stable Semantics for IAFs
	4 Computational Issues
		4.1 Computational Complexity
		4.2 SAT-Based Computational Approach
	5 Related Work
	6 Conclusion
	References
Relevant Epistemic Logic with Public Announcements and Common Knowledge
	1 Introduction
	2 Relational Semantics
	3 A Relational Completeness Result
	4 Information Models
	5 Questions
	6 Conclusion
	References
A Variant with the Variable-Sharing Property of Brady's 4-Valued Implicative Expansion BN4 of Anderson and Belnap's Logic FDE
	1 Introduction
	2 The Matrix MBN4VSP
	3 The Logic BN4VSP
	4 Belnap-Dunn Semantics for BN4VSP
	5 Concluding Remarks
	References
Intrinsic Argument Strength in Structured Argumentation: A Principled Approach
	1 Introduction
	2 Basic Concepts
	3 Principles
	4 Assigning Intrinsic Strength
	5 Aggregation Methods
	6 Properties of Aggregation Methods
	7 Conclusion
	References
How Can You Resolve a Trilemma? - A Topological Approach -
	1 Introduction
	2 Basic Concepts
	3 AF Including One Triangular Unit
		3.1 No Connector
		3.2 One Connector
		3.3 k Connectors
	4 Triangular Units Sharing Nodes
		4.1 AF Including Two triangular units
		4.2 AF Including Three triangular units
		4.3 AF Including k triangular units
		4.4 Acceptance of a Specific Argument
		4.5 N-Lemma
	5 Connected Modules
	6 Related Works
	7 Conclusion
	References
A Multi Attack Argumentation Framework
	1 Introduction
	2 Related Work
	3 Multi Attack Argumentation Frameworks (MAAFs)
		3.1 Classes of Extensions for MAAFs
		3.2 Firm, Restricted and Loose Extensions
	4 Properties of MAAFs
		4.1 Initial Results and Special Cases
		4.2 Relations Among Extension Types, and Existence Results
		4.3 Relations Among Extension Classes
	5 Discussion and Conclusion
	A Appendix
	References
Towards a Sound and Complete Dialogue System for Handling Enthymemes
	1 Introduction
	2 Preliminaries
	3 Dialogue System
	4 Soundness and Completeness
	5 Conclusion
	References
Short Papers and Extended Abstracts
A Henkin-Style Completeness Proof for the Modal Logic S5
	1 Introduction
		1.1 Related Work
		1.2 Lean
	2 Modal Logic
		2.1 The Language
		2.2 The Proof System
		2.3 Semantics
	3 The Completeness Theorem
	References
Base Argumentation as an Abstraction of Deductive Argumentation
	1 Introduction
	2 Preliminaries
		2.1 Abstract Argumentation Framework
		2.2 Tarski's Abstract Logic
		2.3 Deductive Argumentation Framework
	3 Base Argumentation Frameworks
	4 Correspondence Between Base and Deductive Argumentation Frameworks
	5 Conclusion and Future Work
	References
An Argumentative Dialogue System for COVID-19 Vaccine Information
	1 Introduction
	2 Related Work
	3 System Architecture
	4 Argumentation Module
	5 Case Study
	6 Conclusion
	References
Extractive-Abstractive Summarization of Judgment Documents Using Multiple Attention Networks
	1 Introduction
	2 Related Work
	3 Proposed Model
		3.1 Overview
		3.2 Key Sentences Extraction Model
		3.3 Summary Abstraction Model
	4 Data and Experiment
		4.1 Dataset and Evaluation Metric
		4.2 Result
	5 Conclusion and Future Work
	References
A Framework for Intuitionistic Grammar Logics
	1 Introduction
	2 Intuitionistic Grammar Logics
	3 Soundness and Completeness
	4 Conclusion
	References
Choosing a Logic to Represent the Semantics of Natural Language
	1 Introduction
	2 Different Logics
	3 Computation and Lexical Semantics
	4 Word Lists
	5 Experiment
	6 Experiment Validation
	7 Conclusion
	References
The Placeholder View of Assumptions and the Curry–Howard Correspondence (Extended Abstract)
	1 Introduction
	References
Paranegations and the Square of Oppositions
	1 Introduction
	2 The Basic Paralogics and the Square of Oppositions
	3 Synthetic Tableaux Method
		3.1 The Case of CLaN
		3.2 The Case of CLuN
		3.3 The Case of CLoN
	4 Conclusion
	References
Validity Under Assumptions and Modus Ponens
	1 Introduction
	2 Semantics and Validity
		2.1 Semantics
		2.2 Validity
	3 Modus Ponens
	4 Conclusion and Future Work
	References
Entailments with Sentential Predicates
	1 Introduction
	2 Propositional Attitude Operators
	3 Conclusion
	References
Author Index