A Protocol-theoretic Framework for the Logic of Epistemic Norms

Description

This book defines a logical system called the Protocol-theoretic Logic of Epistemic Norms (PLEN), it develops PLEN into a formal framework for representing and reasoning about epistemic norms, and it shows that PLEN is theoretically interesting and useful with regard to the aims of such a framework. In order to motivate the project, the author defends an account of epistemic norms called epistemic proceduralism. The core of this view is the idea that, in virtue of their indispensable, regulative role in cognitive life, epistemic norms are closely intertwined with procedural rules that restrict epistemic actions, procedures, and processes. The resulting organizing principle of the book is that epistemic norms are protocols for epistemic planning and control. The core of the book is developing PLEN, which is essentially a novel variant of propositional dynamic logic (PDL) distinguished by more or less elaborate revisions of PDL’s syntax and semantics. The syntax encodes the procedural content of epistemic norms by means of the well-known protocol or program constructions of dynamic and epistemic logics. It then provides a novel language of operators on protocols, including a range of unique protocol equivalence relations, syntactic operations on protocols, and various procedural relations among protocols in addition to the standard dynamic (modal) operators of PDL. The semantics of the system then interprets protocol expressions and expressions embedding protocols over a class of directed multigraph-like structures rather than the standard labeled transition systems or modal frames. The intent of the system is to better represent epistemic dynamics, build a logic of protocols atop it, and then show that the resulting logic of protocols is useful as a logical framework for epistemic norms. The resulting theory of epistemic norms centers on notions of norm equivalence derived from theories of process equivalence familiar from the study of dynamic and modal logics. The canonical account of protocol equivalence in PLEN turns out to possess a number of interesting formal features, including satisfaction of important conditions on hyperintensional equivalence, a matter of recently recognized importance in the logic of norms, generally. To show that the system is interesting and useful as a framework for representing and reasoning about epistemic norms, the author applies the logical system to the analysis of epistemic deontic operators, and, partly on the basis of this, establishes representation theorems linking protocols to the action-guiding content of epistemic norms. The protocol-theoretic logic of epistemic norms is then shown to almost immediately validate the main principles of epistemic proceduralism. Preface Acknowledgments Contents List of Abbreviations List of Figures List of Tables Part I Epistemic Proceduralism 1 Epistemic Proceduralism Stated 1.1 Introduction 1.1.1 On Epistemic Rationality Norms 1.1.2 On the Logic of Epistemic Norms or Lack Thereof 1.1.3 Toward a Logic of Epistemic Norms 1.1.4 Philosophical Landscape 1.2 Epistemic Proceduralism Stated 1.3 Terminological and Conceptual Groundwork 1.3.1 Epistemic Dynamics and Actions 1.3.2 Labeled Transition Systems 1.3.3 Epistemic Procedures 1.3.4 Epistemic Rationality Norms and Norm-Kernels 1.3.5 Restrictions on Epistemic Dynamics 1.4 Terminological Disputes Set Aside 1.4.1 Epistemic Rationality vs Other Terms of Epistemic Appraisal 1.4.2 Epistemic Factors vs Epistemic Agents 1.4.3 Epistemic vs Non-epistemic Norms 1.4.4 Epistemic Involuntarism 1.4.5 Procedural Epistemology 1.5 Toward the Defense References 2 Epistemic Proceduralism Defended I 2.1 Epistemic Proceduralism Defended 2.2 The First Cluster of Principles (D1) 2.2.1 The Core of the Matter 2.2.2 The Existence and Irreducibility of Dynamic Norms 2.2.2.1 (D1C1.1) Argument from Cases 2.2.2.2 (D1C1.2) Argument from Cases 2.2.2.3 Definitions for Arguments by Construction 2.2.2.4 (D1C1.1C) Argument by Construction 2.2.2.5 (D1C1.3) Argument by Construction 2.2.2.6 (D1C1.4) Argument by Construction 2.2.2.7 (D1C1.5) Argument from the Failure of Reduction Strategies 2.2.2.8 (D1C1.5) Formal Argument 2.2.2.9 (D1C1.6) Construction Rule 2.2.3 The Existence and Irreducibility of Procedural Norms 2.2.3.1 (D1C2 Core) Argument from the Regulative Function of Epistemic Norms 2.2.3.2 (D1C2.1) Argument from Cases 2.2.3.3 (D1C2.2) Argument from Cases 2.2.3.4 (D1C2.3) Argument by Construction 2.2.3.5 (D1C2.4) Derivation from D1C2.9 and D1C2.10 2.2.3.6 (D1C2.4) Argument from the Regulative Function of Epistemic Norms and Epistemic Planning 2.2.3.7 (D1C2.4) Argument from Restrictions on Actions and Processes 2.2.3.8 (D1C2.5) Construction Rule 2.2.3.9 (D1C2.6) Construction Rule 2.2.3.10 (D1C2.7) Construction Rule 2.2.3.11 (D1C2.8) Construction Rule 2.2.3.12 (D1C2.9) Direct Argument 2.2.3.13 (D1C2.10) Direct Argument 2.3 The Second Cluster of Principles (D2) 2.3.1 (D2 Core) Argument from Cases 2.3.2 (D2 Core) Arguments from Epistemic Regulation and Planning 2.3.3 (D2.1)–(D2.3) Arguments from Cases 2.3.4 (D2.4)–(D2.6) Argument from Correlation of Procedural Operations with Path Structures 2.3.5 (D2.7) Construction Rule 2.3.6 Epistemic Norms as Programs or Plans 2.3.7 (D2C1.1–D2C1.4) Argument from Cases 2.4 Toward Further Defense References 3 Epistemic Proceduralism Defended II 3.1 The Logic of Epistemic Rationality Norms 3.1.1 Reasoning with and About Epistemic Norms 3.1.1.1 (D3.1) Direct Argument 3.1.1.2 (D3.2) Arguments from the Regulative Function of Epistemic Norms and Epistemic Deliberation 3.1.1.3 (D3.2) Arguments from Epistemic Planning 3.1.1.4 (D3.2) Arguments from Formal Epistemology 3.1.1.5 (D3C1) Implication from Prior Arguments 3.1.2 The Logic of Epistemic Deontics 3.1.2.1 (D3C2 Core) 3.1.2.2 (D3C2.1) 3.1.2.3 (D3C2.2) 3.1.2.4 (D3C2.3) 3.1.3 The Logic of Norm Application 3.1.3.1 (D3C3 Core) 3.1.3.2 (D3C3.1) 3.1.3.3 (D3C3.2-3) 3.1.3.4 (D3C3.4) 3.1.3.5 (D3C3.5) 3.1.3.6 (D3C3.6) 3.1.3.7 (D3C3.7) 3.2 Epistemic Proceduralism as Criteria on the Logic of Epistemic Norms 3.3 Applying the Criteria of Epistemic Proceduralism 3.3.1 Propositional Dynamic Logic 3.3.2 Dynamic Epistemic Logic 3.3.3 AGM Belief Revision Theory 3.4 From Epistemic Proceduralism to the Protocol-Theoretic Framework References Part II Developing PLEN 4 PLEN: A Protocol-Theoretic Logic of Epistemic Norms 4.1 Introduction 4.1.1 The Protocol-Theoretic Logic of Epistemic Norms (PLEN) and the PLEN Framework 4.2 Technical Development 4.2.1 Syntactic System 4.2.1.1 Syntactic Constructions 4.2.1.2 Important Syntactic Constructions I 4.2.1.3 Important Syntactic Constructions II 4.2.2 Semantic System 4.2.2.1 Execution Rules 4.2.2.2 Truth Rules 4.2.2.3 Validity (Semantic) 4.2.3 Derivation System 4.2.3.1 Execution-Theoretic Rules and Axioms 4.2.3.2 Propositional and Modal Logic 4.2.3.3 Validity (Syntactic) 4.2.4 Metalogic 4.3 Philosophical Development 4.3.1 Philosophical Interpretation 4.3.1.1 Procedural Epistemic Norms Are Protocols, and Protocols in PLEN Are Procedural Epistemic Norms 4.3.1.2 EDGs Are Single-Agent Models of Epistemic Dynamics 4.3.2 Detailed Examples 4.3.2.1 Programming Constructions 4.3.2.2 The Researcher Case 4.3.2.3 The Honest Twin Case 4.3.3 Philosophical Distinctions and Rival Systems 4.3.3.1 Norm Exogeny and Protocol Information 4.3.3.2 The Processes Problem 4.3.3.3 PLEN vs The Processes Problem 4.3.3.4 PLEN vs Rival Systems 4.4 From PLEN to the Revised PLEN Framework Appendix 1 Completeness Soundness Completeness Conjecture PLEN Fischer-Ladner Lemma PLEN Filtration Lemma The Small Model Property and Miscellaneous Steps on the Way to Completeness Proof of Completeness Decidability, Complexity, and Compactness Decidability Conjecture Complexity Conjecture Compactness References 5 The Revised PLEN Framework I: Protocol Equivalence (Useful Lemmata) 5.1 Revising the PLEN Framework 5.2 Protocol Equivalence Relations 0 5.3 Protocol Equivalence Relations I: Non-local Execution-Theoretic Protocol Equivalence 5.3.1 Execution-Theoretic Protocol Equivalence: Meta-Language 5.3.2 Execution-Theoretic Protocol Equivalence: Object-Language Counterparts 5.4 Preliminaries 5.4.1 Process Equivalence Relations 5.4.2 Graph Reduction Operations 5.4.3 Protocol Graphs 5.5 Protocol Equivalence Relations II: Graph-Theoretic Protocol Equivalence 5.5.1 Graph-Theoretic Protocol Equivalence: Meta-Language 5.5.2 Graph-Theoretic Protocol Equivalence: Object Language Counterparts 5.6 Revised Derivation System: The R-Derivation System 5.6.1 Revising the Syntax of PLEN: (ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper L Subscript upper P upper L upper E upper N Superscript upper R) /StPNE pdfmark [/StBMC pdfmarkLPLENRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark) 5.6.2 Revising the Semantics of PLEN: (ps: [/EMC pdfmark [/Subtype /Span /ActualText (upper L Subscript upper P upper L upper E upper N Superscript upper R) /StPNE pdfmark [/StBMC pdfmarkLPLENRps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark) 5.6.3 The R-Derivation System 5.7 Useful Lemmata 5.7.1 Proper Immediate Subprotocols and Well-Foundedness 5.7.1.1 Methodological Observations 5.7.2 Immediate Subprotocol Hierarchies 5.7.3 Implementation Rules 5.7.3.1 Canonical Implementation Rules 5.7.3.2 Implementations and Protocol Graphs 5.7.4 Protocol Graphs and Isomorphism 5.7.4.1 Structural Uniqueness 5.7.4.2 ISOP and EQID Appendix 2 Simultaneous Recursion and Countability Additional Graph Reduction Operations Implementation Rules 5.7.5 Details for SUT Lemma L6 Lemmata Relating Isomorphism and Protocol Graph Sets: ISOPL, ISOP, and EQID References 6 The Revised PLEN Framework II: Protocol Equivalence (Core Results) 6.1 The Theory of Protocol Graph Isomorphism Equivalence 6.1.1 Roadmap of the Core Results of PLEN 6.2 Properties of Protocol Equivalence 6.2.1 Formal Equivalence 6.2.2 PRT 6.3 Protocol Graph Isomorphism Invariance for Regular Constructions 6.3.1 Incremental Graph Reduction Procedure 6.3.2 The ps: [/EMC pdfmark [/Subtype /Span /ActualText (circled plus Subscript ring Superscript pi Baseline) /StPNE pdfmark [/StBMC pdfmarkπps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark Procedure and Protocol Graph Operation ps: [/EMC pdfmark [/Subtype /Span /ActualText (circled plus Subscript ring Superscript pi Baseline) /StPNE pdfmark [/StBMC pdfmarkπps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark 6.3.3 Derivation of the Theorem 6.3.3.1 Modified Lemmata 6.3.3.2 Structural Induction 6.4 Protocol Equivalence and Syntactic Replacement 6.4.1 RGSRT 6.4.2 Graph Syntactic Replacement Theorems 6.5 Granularity 6.5.1 Strictness and Informativeness 6.5.2 Hyperintensional Equivalence 6.6 The Logic of Protocols and Protocol Graph Isomorphism Equivalence Appendix 3 Protocol (Equivalence) Relation Transmission: PRT Protocol Relation Transmission NSTL References 7 The Revised PLEN Framework III: An Adaptable Protocol Logic 7.1 The Revised Protocol Logic 7.2 Standard Metalogic Revised 7.2.1 Revised Soundness Theorem 7.2.2 Revised Completeness? 7.3 Protocol Logic and Distinctive Argument Forms 7.3.1 Regimentation/Formalization of D3 and D3C1: The Protocol-Theoretic Logic of Epistemic Norms I 7.3.1.1 Derivations of Protocol Equivalence 7.3.1.2 Derivations from Protocol Equivalence 7.3.1.3 Dependence, Independence, and Sufficiency 7.4 Investigating Sublogics of Epistemic Norms and Dynamics 7.4.1 Sublogics of PLEN and Theories of Protocol Equivalence 7.5 Modularity and Further Expansions or Revisions 7.5.1 Modularity: Relevant PLEN 7.5.2 Modularity: Conditions on Epistemic States 7.6 Toward the Formalization of Epistemic Proceduralism Appendix 4 Revised Deduction Theorem Revised Completeness: Bits and Pieces Revised Small Model Property Completeness for the R-Derivation System with Bounded Iterations References Part III Applying PLEN 8 Philosophical Results I: A Protocol-Theoretic Logic of Epistemic Deontics, Procedural Knowledge, and Norm Application 8.1 Introduction 8.2 A Protocol-Theoretic Logic of Epistemic Deontics (PLED) 8.2.1 PLED: The Idea 8.2.2 Defining the PLED System 8.2.2.1 The Logic of PLED 8.2.3 Immediate Philosophical Arguments 8.2.4 Protocol-Theoretic Logic and Hyperintensionality 8.2.5 Paradox Resolutions 8.2.5.1 Jorgensen's Dilemma 8.2.5.2 The Necessity of Obligations 8.2.5.3 Free Choice Permissions and Violability 8.2.5.4 The Good Samaritan 8.2.5.5 Conflicting Obligations 8.2.5.6 Chisolm's Paradox 8.2.5.7 The Gentle Murder 8.2.5.8 Paradox of the Miners 8.3 A Protocol-Theoretic Logic of Procedural Knowledge and Norm Application (PLEKNA) 8.3.1 PLEKNA: The Idea 8.3.2 Defining PLEKNA 8.3.3 The Logic of PLEKNA 8.3.4 Some Immediate Virtues 8.4 A Protocol-Theoretic Logic of Epistemic Deontics, Procedural Knowledge, and Norm Application (PLEDKNA) References 9 Philosophical Results II: Representation Theorems and Rule-Following 9.1 Representation Theorems 9.2 Representation Theorem 1 9.2.1 Restrictions on Epistemic Dynamics 9.2.2 Restrictions on Procedural Construction 9.2.3 Representation Theorem 1: Restriction Representation Theorem (RRT) 9.3 Representation Theorem 2 9.3.1 Protocol-Theoretic Norm-Kernels 9.3.2 Representation Theorem 2: Protocol Function Theorem 9.3.2.1 The Protocol Function Theorem 9.4 Rule-Following 9.4.1 The Problems 9.4.2 Rules for Applying Rules 9.4.3 The Solutions 9.5 Representing Epistemic Proceduralism Appendix 5 Reduction Lemma Corollaries of Minor Interest References 10 Philosophical Results III: Formalizing Epistemic Proceduralism 10.1 Adequate Representation Theses 10.2 Cluster D1 and D1C1 10.2.1 Groundwork 10.2.2 D1 and D1C1 Elaboration 10.2.3 D1 and D1C1 Formalization 10.3 Cluster D1C2 10.3.1 D1C2 Elaboration 10.3.2 D1C2 Formalization 10.4 Cluster D2 10.4.1 D2 Elaboration 10.4.2 D2 Formalization 10.5 Cluster D2C1 10.5.1 D2C1 Elaboration 10.5.2 D2C1 Formalization 10.6 Cluster D3 and D3C1 10.6.1 D3 and D3C1 Elaboration 10.6.2 D3 and D3C1 Formalization 10.7 Cluster D3C2 10.7.1 Elaboration of D3C2 10.7.2 Formalization of D3C2 10.8 Cluster D3C3 10.8.1 D3C3 Elaboration 10.8.2 D3C3 Formalization 10.9 For Future Work Reference