Structural Analysis of Non-Classical Logics: The Proceedings of the Second Taiwan Philosophical Logic Colloquium (Logic in Asia: Studia Logica Library)

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: (i) structural modeling of certain philosophical issues in the framework of non-classic logics, such as admissible models for modal logic, structural models for modal epistemology and for counterfactuals, and epistemological models for common knowledge and for public announcements; (ii) conceptual analysis of logical properties of, and formal semantics for, non-classical logics, such as sub-formula property, truthmaking, epistemic modality, behavioral strategies, speech acts and assertions. The structural analysis provided in this volume will appeal not only to graduate students and experts in non-classic logics, but also to readers from a wide range of disciplines, including computer science, cognitive science, linguistics, game theory and theory of action, to mention a few. Preface 7 Contents 12 Contributors 14 1 Semantical Approach to Cut Elimination and Subformula Property in Modal Logic 15 1.1 Introduction 15 1.2 Sequent Systems for Some Modal Logics 16 1.3 Kripke Completeness, Finite Model Property and Finite Embeddability Property 18 1.4 Takano's Approach to Subformula Property 21 1.5 Cut Elimination 23 1.6 Quasi-embeddings and Downward Saturation 26 References 28 2 Ultraproducts of Admissible Models for Quantified Modal Logic 30 2.1 Introduction 30 2.2 Admissible Models 32 2.3 Ultraproducts of Premodels 35 2.4 Łoś' Theorem 37 2.5 Compactness 41 2.6 Propositional Logic 42 2.7 Quantified Logics 43 2.8 Strong Completeness with the Barcan Formulas 45 2.9 One Universal Domain 48 References 49 3 Logic and/of Truthmaking 50 3.1 Introduction 50 3.2 Truthmaker Theory 51 3.3 Logic and Truthmaking 52 3.3.1 Williamson's Argument 52 3.3.2 Objections to the Argument 54 3.4 The Logic of Truthmaker Theory 59 3.4.1 Some (conflicting) Truthmaking Principles 59 3.4.2 Two Approaches to Truthmaking 61 3.4.3 Moving Forward 63 References 67 4 Structural Models for Williamson's Modal Epistemology 69 4.1 Introduction 69 4.2 Williamson's Account and Its Problems 72 4.3 Structural Models 75 4.4 Modal Epistemology Naturalised 86 References 92 5 Motivating the Causal Modeling Semantics of Counterfactuals, or, Why We Should Favor the Causal Modeling Semantics over the Possible-Worlds Semantics 94 5.1 Introduction 94 5.2 The Possible-Worlds Semantics 95 5.3 Troubling Cases and Refinements 96 5.4 Backtracking Counterfactuals 101 5.5 The Causal Modeling Semantics 104 5.6 Backtracking Counterfactuals Revisited 113 5.7 Troubling Cases Revisited 116 5.8 Conclusion 119 References 120 6 The Meaning of Epistemic Modality and the Absence of Truth 122 6.1 Introduction: A Puzzle About `Or' and `Might' 123 6.2 Recent Explanations of the Conjunctive `Or' 125 6.3 New Explanation 126 6.3.1 Acceptability at a Information State 126 6.3.2 Semantics of `Might' and `Or' 127 6.3.3 Conjunctive `Or' Explained 129 6.4 Acceptability-Conditional Semantics 130 6.5 A New Puzzle and Its Solution 133 6.6 Which Declarative Sentences Lack Truth Conditions? 134 6.7 Concluding Remarks 136 References 141 7 Revising a Labelled Sequent Calculus for Public Announcement Logic 142 7.1 Introduction 142 7.2 Kripke Semantics and Axiomatization of PAL 144 7.2.1 Kripke Semantics of PAL 144 7.2.2 Hilbert-Style Axiomatization of PAL 146 7.3 Sequent Calculus for PAL 147 7.3.1 G3PAL 147 7.3.2 Problems of G3PAL 149 7.4 Revising G3PAL 150 7.4.1 Revised Sequent Calculus GPAL 151 7.4.2 All Theorems of HPAL are provable in GPAL+ 155 7.4.3 Cut Elimination of GPAL+ 156 7.5 Soundness of GPAL 158 7.6 Completeness of GPAL for Link-Cutting Semantics 161 7.7 Conclusion 167 References 167 8 Logics for Dynamic Epistemic Behavioral Strategies 169 8.1 Introduction 169 8.2 Game Structures 172 8.2.1 Incomplete and Imperfect Information Games 172 8.2.2 Strategies and Copies of the Same Game Forest 175 8.3 A Variation of PLCC 176 8.3.1 Event Models for Game Structures 178 8.4 Event Models for a Given Game Structure 181 8.4.1 Epistemic Behavioral Strategies 181 8.4.2 Involving Multiple Strategy Profiles 184 8.5 Payoffs and Rationality 187 8.5.1 Comparing Preference or Utility of Nodes 188 8.5.2 Comparing Event Models 190 8.6 Conclusion 190 References 191 9 Measurement-Theoretic Foundations of Observational-Predicate Logic 193 9.1 Motivation 193 9.2 Statistical Consistency: Strong Statistical Transitivity (SST) 198 9.3 Measurement-Theoretic Analysis of JNDs and Semiorders 198 9.4 Observational Predicate Logic (OPL) 201 9.4.1 Language of OPL 201 9.4.2 Semantics of OPL 201 9.4.3 Metalogic of OPL 204 9.5 Discussion: Higher Order Vagueness 205 9.5.1 Wright's Argument that Higher Order Vagueness Is per se Paradoxical 205 9.5.2 Sentential Operator Versus Predicate Symbol 206 9.6 Concluding Remarks 207 References 208 10 Channel Theoretic Reflections on Dynamic Logics of Speech Acts 210 10.1 Introduction 210 10.2 Logical Dynamics of Speech Acts 212 10.3 Actions in Channel Theory 216 10.4 Acts of Commanding in Channel Theory 220 10.5 Channel Theoretic Reflections on DMDL+III and Its Possible Extensions 225 References 230 11 Constructive Embedding from Extensions of Logics of Strict Implication into Modal Logics 231 11.1 Introduction 231 11.2 Kripke Semantics for Extensions of F 233 11.3 Labelled Sequent Calculus for F 234 11.3.1 Labelled Formalism 234 11.4 Extensions of Logic of Strict Implications 237 11.4.1 Intermediate Logics 237 11.4.2 Extensions of Basic Propositional Logic 238 11.4.3 Logics of Strict Implication 239 11.5 Admissibility of Cut 240 11.6 Constructive Embedding from Extensions F into Modal Logics 245 11.6.1 Labelled Sequent Calculus for K 246 11.6.2 Embedding Theorem 246 11.7 Soundness and Completeness of G3F(m)ast for Kripke Semantics 252 11.7.1 Soundness 252 11.7.2 Completeness 253 11.8 Further Direction 257 References 258 12 Common Knowledge and the Knowledge Account of Assertion 260 12.1 Introduction 260 12.2 Common Knowledge in the Framework of Orthodox Epistemic Logic of Knowledge 263 12.3 Two Main Problems with the Orthodox Semantic 266 12.3.1 The Legitimacy of the Posit Accessibility Relations in Kripke's Models 267 12.3.2 A Davidsonian Challenge 269 12.4 Toward a Communication-Oriented Approach to Common Knowledge 270 12.5 The Appeal to the Knowledge Account of Assertion 272 12.6 TWC-Models and the Assertion Account of Common Knowledge 279 12.6.1 TWC-models 279 12.6.2 The Semantics 281 12.6.3 Basic Assumptions Validated and Some Other Results 281 12.6.4 A Justification of (CKA) 281 12.7 Concluding Remarks 283 References 284 Front Matter....Pages i-xv Semantical Approach to Cut Elimination and Subformula Property in Modal Logic....Pages 1-15 Ultraproducts of Admissible Models for Quantified Modal Logic....Pages 17-36 Logic and/of Truthmaking....Pages 37-55 Structural Models for Williamson’s Modal Epistemology....Pages 57-81 Motivating the Causal Modeling Semantics of Counterfactuals, or, Why We Should Favor the Causal Modeling Semantics over the Possible-Worlds Semantics....Pages 83-110 The Meaning of Epistemic Modality and the Absence of Truth....Pages 111-130 Revising a Labelled Sequent Calculus for Public Announcement Logic....Pages 131-157 Logics for Dynamic Epistemic Behavioral Strategies....Pages 159-182 Measurement-Theoretic Foundations of Observational-Predicate Logic....Pages 183-199 Channel Theoretic Reflections on Dynamic Logics of Speech Acts....Pages 201-221 Constructive Embedding from Extensions of Logics of Strict Implication into Modal Logics....Pages 223-251 Common Knowledge and the Knowledge Account of Assertion....Pages 253-278