Nonclassical Logics and Their Applications: Post-proceedings of the 8th International Workshop on Logic and Cognition (Logic in Asia: Studia Logica Library)

✍ Scribed by Shier Ju (editor), Alessandra Palmigiano (editor), Minghui Ma (editor)

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 159
• Series: Logic in Asia: Studia Logica Library
• Edition: 1st ed. 2020
• Category: Library

✦ Synopsis

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science.

 

This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions.

Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com

✦ Table of Contents

Preface
Contents
Hyperstates of Involutive MTL-Algebras that Satisfy (2x)2=2(x2)
1 Motivation
2 Abelian ell-Groups, MV-Algebras and Their States
3 From ell-Monoids to ell-Groups and Hoops
4 States of Prelinear Semihoops
5 States of IBP0-Algebras and Their Representation
6 Conclusions and Future Work
References
The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms
1 Introduction
1.1 Some Foundational Issues
1.2 Specification Styles
1.3 General Motivation
1.4 This Paper's Categorical Investments
1.5 This Paper's Categorical Dividends
1.6 Explicitness for Novice Category Theorists and Others
1.7 Organization
2 The Category of Node-and-Choice Forms
2.1 Objects
2.2 Morphisms
2.3 The Category NCF
2.4 No-Absentmindedness and Perfect-Information
3 The Subcategory of Choice-Sequence Forms
3.1 Objects
3.2 Isomorphic Enclosure
3.3 More About No-Absentmindedness
4 The Subcategory of Choice-Set Forms
4.1 Objects
4.2 Isomorphic Enclosure
4.3 More About Perfect-Information
5 Further Remarks
5.1 Deducing Consequences from an Isomorphic Enclosure
5.2 Future Research
References
About the Temporal Logic of the Lexicographic Products of Unbounded Dense Linear Orders: A New Study of Its Computability
1 Introduction
2 Products of Unbounded Dense Linear Orders
3 Syntax and Semantics
4 Mosaics
5 Maps
6 Correctness and Completeness of the Mosaic Method
6.1 Correctness
6.2 Completeness
7 Decidability and Complexity
8 Conclusion
References
Contact Logic is Finitary for Unification with Constants
1 Introduction
2 Syntax
3 Semantics
4 About Classes of Frames
5 Unifiability
6 Examples
7 Monomials and Polynomials
8 Equivalence Relations Between Tuples of Bits
9 Equivalence Relations Between Formulas
10 Unification Type
11 Conclusion
References
A Multi-agent Default Theory of Permission
1 Multi-agent Prioritized Default Theory
1.1 Agent-Relative Defeasible Obligations
2 Three Types of Permissions
2.1 Weak Permissions
2.2 Explicit Permissions
2.3 Tacit Permissions
2.4 A Fourth Type: Protected Permissions
3 Conclusion
References
Algebraic Semantics for Hybrid Logics
1 Introduction
2 Preliminaries
3 Algebraic Semantics
3.1 Algebraic Semantics for the Language mathcalH
3.2 Algebraic Semantics for the Language mathcalH(@)
3.3 Duality with Two Sorted-General Frames
4 Algebraic Completeness: Axiomatic Extensions of H and H+
4.1 Completeness of H oplusΣ
4.2 Completeness of H+oplusΣ
5 Algebraic Completeness: Axiomatic Extensions of H(@) and H+(@)
5.1 Completeness of H(@)oplusΣ
5.2 Algebraic Completeness of H+(@)oplusΣ
6 Global Completeness
7 Conclusion
References