Knowledge, Proof and Dynamics: The Fourth Asian Workshop on Philosophical Logic (Logic in Asia: Studia Logica Library)

✍ Scribed by Fenrong Liu (editor), Hiroakira Ono (editor), Junhua Yu (editor)

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 219
• Category: Library

✦ Synopsis

This volume gathers selected papers presented at the Fourth Asian Workshop on Philosophical Logic, held in Beijing in October 2018. The contributions cover a wide variety of topics in modal logic (epistemic logic, temporal logic and dynamic logic), proof theory, algebraic logic, game logics, and philosophical foundations of logic. They also reflect the interdisciplinary nature of logic – a subject that has been studied in fields as diverse as philosophy, linguistics, mathematics, computer science and artificial intelligence. More specifically. The book also presents the latest developments in logic both in Asia and beyond.

✦ Table of Contents

Preface
Contents
Contributed Papers
The Modal Logics of the Poison Game
1 Introduction
2 mathcalML
3 mathcalPML
4 mathcalPSL
5 Conclusion
References
A Logical Characterization of the Continuous Bar Induction
1 Introduction
2 Preliminary
3 A Logical Characterization of c-BI
4 LLPO and Fragments of Bar Induction
References
Unary and Two-Variable Interval Logics
1 Introduction
2 Two-Variable Logics and Interval Logics
2.1 Unambiguous Interval Temporal Logic
2.2 Lookaround Interval Temporal Logic
2.3 Halpern–Shoham Logics
3 Interval Logics with Invariance
3.1 Modelling Addition
3.2 Defining Circuits
3.3 Defining Monomials
4 Staying Within Two-Variable Between Logic
5 Drawing Some Conclusions
References
Logics for Knowability Paradox with a Non-normal Possibility Operator
1 Introduction
2 Syntax and Sequent Calculi for Knowability Paradox
2.1 Syntax
2.2 The Systems of G1Kc and G1Ki
3 Hilbert Systems and Their Semantics of Intuitionistic Bimodal Logic for Knowability Paradox
3.1 Hilbert Systems and Intuitionistic Kripke Semantics
3.2 Strong Completeness of HK i
4 Glivenko–Kuroda Embedding and Cut Elimination
4.1 Glivenko–Kuroda Theorem: Embedding of G1K c+ into G1K i+
4.2 Cut-Elimination Theorem of G1K i
4.3 Cut-Elimination of G1K c
5 Craig Interpolation Theorems
5.1 Craig Interpolation Theorem of G1K i
6 Decidability of G1Ki and G1Kc
7 Conclusion and Further Direction
Appendix
References
Local Fact Change Logic
1 Introduction
1.1 Related Work
2 Propositional Fact Change
2.1 Validities, Completeness, Reduction for PFC
3 Local Fact Change Logic
3.1 Definition of LFC
3.2 Application of LFC: Nash Equilibria
3.3 Some Validities in LFC
3.4 Particularised Fact Change
4 Undecidability of Local Fact Change Logic
4.1 Generalised Assignment Models
5 Expressive Power
6 Conclusion and Further Work
References
Solution Complexity of Local Variants of Sabotage Game
1 Introduction
2 Preliminary
3 Local Link-Cutting Variant
3.1 A Solution Algorithm
3.2 Correctness Proof of the Algorithm
4 Local Node-Deleting Variant
4.1 PSPACE Upper Bound by an Alternating Algorithm
4.2 Reduction from QBF
5 Poison Game
5.1 PSPACE Upper Bound by an Alternating Algorithm
5.2 Reduction from QBF
6 Logical Aspect
7 Related Work
8 Conclusion
References
Invited Papers
Graph Games and Logic Design
1 Two Graph Games
1.1 Traveling Along a Graph
1.2 Travel and Damage
2 Modified Scenarios
2.1 Modified Travel Games
2.2 Modified Sabotage Games
3 Parameters for Game Design
4 Logics for Graph Games
5 Digression: Imperfect Information
6 Conclusion
References
De Re, De Dicto, and Binding Modalities
1 Introduction
2 Binding Modalities—De Re/De Dicto
3 Binding Modalities—Syntax
4 Binding Modalities—Semantics
5 De Re/De Dicto Conversions
6 Binding Modalities—Varying Domain Axiomatics
7 Monotonicity and Anti-monotonicity
8 Soundness
9 Completeness
10 Conclusion
References
Refutation Systems: An Overview and Some Applications to Philosophical Logics
1 Introduction
2 Refutation Systems: Basic Concepts
2.1 Semantic Versus Deductive Refutability
2.2 Refutation Rules and Systems
3 Refutation Systems: An Overview
3.1 Beginning and Early Work on Refutation Systems
3.2 Overview of Refutation Systems in Classical Logic
3.3 Gentzen-Style Refutation Systems
3.4 Refutation Systems for Non-validity in the Finite
3.5 Refutation Systems for Intuitionistic and Modal Logics
3.6 Refutation Systems for Other Non-classical Logics
3.7 Systems Combining Proofs and Refutations
3.8 Further General References on Refutation Systems
4 Refutation Systems Versus Deductive Systems
4.1 Tableaux Versus Refutation Systems
4.2 Inverse Refutation Systems
4.3 Gentzen-Style Sequent Refutation Systems
5 Some Applications to Non-classical Logics
5.1 Defining Non-classical Logics via Refutability
6 Concluding Remarks
References
Influence in Different Network Structures
1 Introduction
2 Belief Updates and Social Influence
2.1 Friends Influence
2.2 Language Splitting
2.3 Expert Influence
3 Influence and Coordination in Networks
3.1 Expected Influence
3.2 Belief Conflict and Coordination Equilibria
3.3 Different Networks
4 Simulating Social Power
5 Conclusion
References