Cover; Half-title; Series information; Title page; Copyright information; Dedication; 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 J[sub(0)], 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 Logics2.7.1 K4[sup(3)] and J4[sup(3)]; 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 J[sub(0)] 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 Semantics4.2 Fitting Models; 4.3 Soundness Examples; 4.3.1 J(CS); 4.3.2 LP; 4.3.3 K4[sup(3)] and J4[sup(3)]; 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 J4[sup(3)]; 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 Logics5 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 Constructively7.8 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 Classical logic is concerned, loosely, with the behaviour of truths. Epistemic logic similarly is about the behaviour of known or believed truths. Justification logic is a theory of reasoning that enables the tracking of evidence for statements and therefore provides a logical framework for the reliability of assertions. This book, the first in the area, is a systematic account of the subject, progressing from modal logic through to the establishment of an arithmetic interpretation of intuitionistic logic. The presentation is mathematically rigorous but in a style that will appeal to readers from a wide variety of areas to which the theory applies. These include mathematical logic, artificial intelligence, computer science, philosophical logic and epistemology, linguistics, and game theory | 
