Temporal Logic

In: LEP Library of Exact Philosophy 3

Abstract

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.

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Temporal logic

In: Library of exact philosophy 3

Rescher, Nicholas

Rescher, Nicholas

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