Justification Logic: Reasoning with Reasons (Cambridge Tracts in Mathematics)

Justification Logic: Reasoning with Reasons
Contents
Introduction
	1 What Is This Book About?
	2 What Is Not in This Book?
1 Why Justification Logic?
	1.1 Epistemic Tradition
	1.2 Mathematical Logic Tradition
	1.3 Hyperintensionality
	1.4 Awareness
	1.5 Paraconsistency
2 The Basics of Justification Logic
	2.1 Modal Logics
	2.2 Beginning Justification Logics
	2.3 J0, the Simplest Justification Logic
	2.4 Justification Logics in General
	2.5 Fundamental Properties of Justification Logics
	2.6 The First Justification Logics
	2.7 A Handful of Less Common Justification Logics
		2.7.1 K4³ and J4³
		2.7.2 S5 and JT45
		2.7.3 Sahlqvist Examples
		2.7.4 S4:2 and JT4:2
		2.7.5 KX4 and JX4
3 The Ontology of Justifications
	3.1 Generic Logical Semantics of Justifications
	3.2 Models for J0 and J
	3.3 Basic Models for Positive and Negative Introspection
	3.4 Adding Factivity: Mkrtychev Models
	3.5 Basic and Mkrtychev Models for the Logic of Proofs LP
	3.6 The Inevitability of Possible Worlds: Modular Models
	3.7 Connecting Justifications, Belief, and Knowledge
	3.8 History and Commentary
4 Fitting Models
	4.1 Modal Possible World Semantics
	4.2 Fitting Models
	4.3 Soundness Examples
		4.3.1 J(CS)
		4.3.2 LP
		4.3.3 K4³ and J4³
		4.3.4 S5 and JT45
		4.3.5 Sahlqvist Examples
		4.3.6 S4:2 and JT4:2
		4.3.7 KX4 and JX4
		4.3.8 A Remark about Strong Evidence Functions
	4.4 Canonical Models and Completeness
		4.4.1 Canonical Modal Logics
		4.4.2 Canonical Justification Models
		4.4.3 Strong Evidence and Fully Explanatory
	4.5 Completeness Examples
		4.5.1 LP and Sublogics
		4.5.2 J4³
		4.5.3 JT45
		4.5.4 Sahlqvist Examples
		4.5.5 S4:2 and JT4:2
		4.5.6 KX4 and JX4
	4.6 Formulating Justification Logics
5 Sequents and Tableaus
	5.1 Background
	5.2 Classical Sequents
	5.3 Sequents for S4
	5.4 Sequent Soundness, Completeness, and More
	5.5 Classical Semantic Tableaus
	5.6 Modal Tableaus for K
	5.7 Other Modal Tableau Systems
	5.8 Tableaus and Annotated Formulas
	5.9 Changing the Tableau Representation
6 Realization – How It Began
	6.1 The Logic LP
	6.2 Realization for LP
	6.3 Comments
7 Realization – Generalized
	7.1 What We Do Here
	7.2 Counterparts
	7.3 Realizations
	7.4 Quasi-Realizations
	7.5 Substitution
	7.6 Quasi-Realizations to Realizations
	7.7 Proving Realization Constructively
	7.8 Tableau to Quasi-Realization Algorithm
	7.9 Tableau to Quasi-Realization Algorithm Correctness
	7.10 An Illustrative Example
	7.11 Realizations, Nonconstructively
	7.12 Putting Things Together
	7.13 A Brief Realization History
8 The Range of Realization
	8.1 Some Examples We Already Discussed
	8.2 Geach Logics
	8.3 Technical Results
	8.4 Geach Justification Logics Axiomatically
	8.5 Geach Justification Logics Semantically
	8.6 Soundness, Completeness, and Realization
	8.7 A Concrete S4:2/JT4:2 Example
	8.8 Why Cut-Free Is Needed
9 Arithmetical Completeness and BHK Semantics
	9.1 Arithmetical Semantics of the Logic of Proofs
	9.2 A Constructive Canonical Model for the Logic of Proofs
	9.3 Arithmetical Completeness of the Logic of Proofs
	9.4 BHK Semantics
	9.5 Self-Referentiality of Justifications
10 Quantifiers in Justification Logic
	10.1 Free Variables in Proofs
	10.2 Realization of FOS4 in FOLP
		10.2.1 Implications for First-Order BHK Semantics
	10.3 Possible World Semantics for FOLP
		10.3.1 The Ideas Informally
		10.3.2 FOLP Fitting Models
		10.3.3 Nonvalidity Examples
		10.3.4 Soundness
		10.3.5 Language Extensions
		10.3.6 The Canonical Fitting Model
		10.3.7 Completeness
		10.3.8 Fully Explanatory Models
		10.3.9 Mkrtychev Models
	10.4 Arithmetical Semantics for FOLP
		10.4.1 Free Variables in First-Order Derivations
		10.4.2 Basic Semantics: Derivations from Hypotheses in PA
		10.4.3 Completeness Is Not Attainable
		10.4.4 Limitations of Provability Semantics
11 Going Past Modal Logic
	11.1 Modeling Awareness
	11.2 Precise Models
	11.3 Justification Awareness Models
	11.4 The Russell Scenario as a JAM
		11.4.1 Closure Conditions for Acceptance and Knowledge-Producing Predicates
		11.4.2 Can Russell’s Scenario Be Made Modal?
	11.5 Kripke Models and Master Justification
	11.6 Conclusion
References
Index