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The Road to Universal Logic; Preface; References; Contents; Contributors; Ibn Sina's Two-Partite Versus Nine-Partite Logicography; 1 Introduction; 2 Aristotle's Books on Logic; 3 Logic in Ibn Sina's Shifa (= Healing); 4 Logic in Ibn Sina's al-Isharat wat-Tanbihat (= Remarks and Admonitions); 5 A Comparison Between Logic in Shifa and Logic in Isharat; 6 Ibn Sina's Reasons on Changing the Structure of Logic and the Style of Logicography; 6.1 Dividing Knowledge into Conception and Assent; 6.2 Study of Categories as a Part of First Philosophy
7 Two-Partite Logic Versus Nine-Partite Logic in the Islamic Tradition8 Main Features and Advantages of Ibn Sina's Two-Partite Methodology in Logicography; References; Homotopical Categories of Logics; 1 Introduction; 2 Categories of Logics; 2.1 Signatures; 2.2 Logics; 3 Abstract Homotopy Theory; 3.1 Simplicial Sets and Nerves; 3.2 Localization of Categories and Homotopy (Co)limits; 3.2.1 Localizing Categories; 3.2.2 Homotopy (Co)limits; 3.3 Simplicial Categories, Simplicial Localizations and Homotopy (Co)limits; 3.3.1 The Hammock Localization; 3.3.2 Homotopy Category of a Simplicial Category
3.3.3 Homotopy (Co)limits Revisited3.3.4 Simplicial Categories from 2-Categories; 3.4 Equivalences of Simplicial Categories and (infty,1)-Categories; 3.5 Models and Computation of Homotopy (Co)limits; 3.5.1 The Homotopy Theory of Homotopy Theories; 4 (infty,1)-Categories of Logics; 4.1 Weak Equivalences; 4.2 The Hammock Localization of Hilb; 4.3 The 2-Categorical Localization of Log; 4.3.1 Logstrict2-cat Versus Log2-cat; 4.3.2 Homotopy Limits in Log2-cat; 4.3.3 Homotopy Colimits in Log2-cat; 5 Vista; 5.1 Further Studies of Categories of Logics; 5.2 Invariants of Logics
5.3 Refined Categories of Logics from Proof Theory5.4 Comparing Paradigms of Logic; 6 Conclusion; References; Semi-implication: A Chapter in Universal Logic; 1 Introduction; 2 Preliminaries; 3 The Relevant Deduction Property (RDP); 4 The Minimal Logics with the RDP; 5 CL and the Classical Equivalence; 6 The Notion of Semi-implication; 7 Semi-implication in Special Types of Matrices; References; A Formal Framework for Hypersequent Calculi and Their Fibring; 1 Introduction; 2 The Category of Formal Hypersequent Calculi; 3 Unconstrained Fibring of Hypersequent Calculi
4 Admissible and Derivable Rules and the Rule Elimination Property5 Preservation Features and Translating Derivations; 6 Extension to Constrained Fibring; 7 The Non-commutative Case; 8 Hypersequent Calculi and Hypertranslations; 9 Concluding Remarks; References; Investigating Knowledge and Opinion; 1 Preliminaries; 2 Introduction; 3 The Spectrum of True Beliefs; 4 The Spectra of Certainty; 5 Senses of `Objective' and `Subjective'; 6 Broad and Narrow Senses of `Believe'; 7 Certitude and Certainty; 8 The Spectra of Certitude; 9 Certain Knowledge; 10 Speaking of Propositional Knowledge
7 Two-Partite Logic Versus Nine-Partite Logic in the Islamic Tradition8 Main Features and Advantages of Ibn Sina's Two-Partite Methodology in Logicography; References; Homotopical Categories of Logics; 1 Introduction; 2 Categories of Logics; 2.1 Signatures; 2.2 Logics; 3 Abstract Homotopy Theory; 3.1 Simplicial Sets and Nerves; 3.2 Localization of Categories and Homotopy (Co)limits; 3.2.1 Localizing Categories; 3.2.2 Homotopy (Co)limits; 3.3 Simplicial Categories, Simplicial Localizations and Homotopy (Co)limits; 3.3.1 The Hammock Localization; 3.3.2 Homotopy Category of a Simplicial Category
3.3.3 Homotopy (Co)limits Revisited3.3.4 Simplicial Categories from 2-Categories; 3.4 Equivalences of Simplicial Categories and (infty,1)-Categories; 3.5 Models and Computation of Homotopy (Co)limits; 3.5.1 The Homotopy Theory of Homotopy Theories; 4 (infty,1)-Categories of Logics; 4.1 Weak Equivalences; 4.2 The Hammock Localization of Hilb; 4.3 The 2-Categorical Localization of Log; 4.3.1 Logstrict2-cat Versus Log2-cat; 4.3.2 Homotopy Limits in Log2-cat; 4.3.3 Homotopy Colimits in Log2-cat; 5 Vista; 5.1 Further Studies of Categories of Logics; 5.2 Invariants of Logics
5.3 Refined Categories of Logics from Proof Theory5.4 Comparing Paradigms of Logic; 6 Conclusion; References; Semi-implication: A Chapter in Universal Logic; 1 Introduction; 2 Preliminaries; 3 The Relevant Deduction Property (RDP); 4 The Minimal Logics with the RDP; 5 CL and the Classical Equivalence; 6 The Notion of Semi-implication; 7 Semi-implication in Special Types of Matrices; References; A Formal Framework for Hypersequent Calculi and Their Fibring; 1 Introduction; 2 The Category of Formal Hypersequent Calculi; 3 Unconstrained Fibring of Hypersequent Calculi
4 Admissible and Derivable Rules and the Rule Elimination Property5 Preservation Features and Translating Derivations; 6 Extension to Constrained Fibring; 7 The Non-commutative Case; 8 Hypersequent Calculi and Hypertranslations; 9 Concluding Remarks; References; Investigating Knowledge and Opinion; 1 Preliminaries; 2 Introduction; 3 The Spectrum of True Beliefs; 4 The Spectra of Certainty; 5 Senses of `Objective' and `Subjective'; 6 Broad and Narrow Senses of `Believe'; 7 Certitude and Certainty; 8 The Spectra of Certitude; 9 Certain Knowledge; 10 Speaking of Propositional Knowledge