Temporal Logic

I The Background of Temporal Logic.- II Topological Logic.- 1. Introduction.- 2. The P-Operator.- 3. Three Basic Axioms.- 4. The Relation of P-Unqualified to P-Qualified Formulas: The Preferred Position ? : A Fourth Axiom.- 5. The Iteration of P: A Fifth Axiom and the Two Systems PI and PII.- 6. The Possible Worlds Interpretation of Topological Logic.- III Fundamental Distinctions for Temporal Logic.- 1. The Temporal Equivocality of IS.- 2. Translating Temporal to Atemporal IS.- 3. Temporally Definite and Indefinite Statements.- 4. The Implicit Ubiquity of “Now” in Tensed Statements.- 5. Dates and Pseudo-Dates.- 6. Times of Assertion.- 7. Two Styles of Chronology.- IV The Basic System R of Temporal Logic.- 1. The Concept of Temporal Realization.- 2. The Temporal Transparency of “Now”.- 3. Temporal Homogeneity.- 4. Axioms for the Logical Theory of Chronological Propositions.- 5. Temporal and Topological Logic.- 6. The Completeness and Decidability of R.- V The Introduction of Tense Operators.- 1. Presentness and Precedence.- 2. Tense.- VI The System Kt of Minimal Tense Logic.- 1. The Problem of a Minimal Tense Logic.- 2. Semantics for Tense Logic.- 3. Semantic Tableaux.- 4. The Completeness of Kt.- 5. Some Corollaries.- 6. Completeness of Kt with Respect to R.- VII Branching Time: The System Kb.- 1. Branching Structures.- 2. The Concept of an Open Future.- 3. The Logic of Branching Time.- 4. Axiomatization of Kb.- 5. Semantic Tableaux.- 6. Systematic Tableaux.- 7. Completeness Proof for Kb.- VIII Linear Time: The System Kl and Its Variants.- 1. The Logic of Linear Time, Kl.- 2. Extensions of Kl.- IX Additive Time: The Systems R? and R?±.- 1. Temporal-Groups and the System R?.- 2. Additive Temporal Logic and the System R?±.- X Metric Time and Chronological Logic: The System R+.- 1. The Concept of Metric Time.- 2. Deriving a U-Relation from the Metric.- 3. The System R+.- 4. “Distance” into Past and Future.- 5. Archimedeanism.- 6. Linear Realizability.- XI Tense Logical Characterizability and Definability.- 1. Expressibility and Characterizability.- 2. Tense-Logical Definability.- XII Temporal Modality.- 1. The Tensed Interpretation of Modality.- 2. Modality in Tense Logic.- 3. Further Definitions of Modality.- XIII Temporally Conditioned Descriptions and the Concept of Temporal Purity.- 1. Temporally Conditioned Descriptions.- 2. Chronological Purity.- 3. The “Purely Phenomenological” Characterization of the Occurrences of a Moment.- 4. The Absolute vs. the Relative Conception of Time.- XIV The Theory of Processes.- 1. What is a Process?.- 2. The Representation of Processes: Process Implications.- 3. Activities and Processes: Some Applicable Distinctions.- 4. Quasi-Processes: On Coming to Be and Passing Away.- 5. Stochastic vs. Deterministic Processes.- 6. Stochastic Processes and Branching Time.- 7. The Structure of Events.- XV The Logic of World States.- 1. The Concept of a World State.- 2. Some Further Perspectives on Instantaneous World States.- 3. The Concept of a World History.- 4. Development of R-calculi Within Tense Logic.- XVI The Dimensionality of Time.- XVII The “Master Argument” of Diodorus and Temporal Determinism.- 1. The “Master Argument”.- 2. Necessity and Determinism in the Context of the “Master Argument”.- 3. Evading the Deterministic Conclusion of the “Master Argument”.- 4. The Groundwork of a 3-Valued Conception of Temporal Truth.- 5. Alternative Futures and Future Contingency.- 6. Temporal Determination.- 7. Nomological Necessitation.- XVIII Many-Valued Approaches to Temporal Logic.- 1. A Mode of “Three-Valued” Tense Logic.- 2. A Many-Valued Articulation of Temporal Logic.- 3. A Three-Valued Tense Logic: Semantic Considerations.- 4. Generalizing the Preceding Approach.- XIX Propositional Quantification in Tensed Statements.- XX Quantification, Temporal Existence, and Identity.- 1. Individuals and Quantifiers.- 2. Quantification and Temporal Modality.- 3. Quantified Tense Logic.- 4. Temporal Change, Identity, and Leibniz’ Law.- 5. Alternative Histories in Branching Time.- 6. Quantified Modal Logic in Branching Time.- Appendix I A Summary of Axiom Systems for Topological, Temporal and Modal Logics.- Appendix II The Modal Structure of Tense-Logical Systems.- Bibliography of Temporal Logic.- A. Chronological Listing.- B. Author Listing (Alphabetical).- Index of Names.