Temporal LogicSpringer Science & Business Media, 06/12/2012 - 273 páginas This book is an introduction to temporal logic, a now flourishing branch of philosophical logic whose origin is of recent date, its main impetus having been provided by the publication in the late 1950s of A. N. PRIOR'S pioneering book, Time and Modality (Oxford, The Clarendon Press, 1957). Virtually all work in the field to around 1966 is surveyed in PRIOR'S elegant treatise Past, Present and Future (Oxford, The Clarendon Press, 1967). In consequence, it is no simple matter to write a comprehensive book on the subject with out merely rehearsing material already dealt with in PRIOR'S works. We believe, however, that the present book succeeds in this difficult endeavor because it approaches established materials from wholly novel points of departure, and is thus able to attain new perspectives and achieve new results. Its introductory character notwithstanding, the present work is consequently in substantial measure devoted to an exposition of new findings and a demonstration of new results. Parts of the book have been published previously. Chapter II is a modified version of an article of the same title by N. RESCHER and JAMES GARSON in The Journal of Symbolic Logic (vol. 33 [1968], pp.537-548). And Chapter XIII is a modified version of the article "Temporally Conditioned Descriptions" by N. RESCHER and JOHN ROBISON in Ratio, vol. 8 (1966), pp. 46-54. The authors are grateful to Professors GARSON and ROBISON, and to the editors of the jounal involved, for their permission to use this materials here. |
Índice
1 | |
4 | |
Chapter II | 13 |
Three Basic Axioms | 14 |
The Preferred Position A Fourth Axiom | 16 |
A Fifth Axiom and the Two Systems PI and PII | 17 |
The Possible Worlds Interpretation of Topological Logic | 21 |
Chapter III | 23 |
The Concept of an Open Future | 70 |
Axiomatization of Kɩ | 76 |
Completeness Proof for Kь | 83 |
Extensions of K | 91 |
Chapter IX | 98 |
Deriving a URelation from the Metric | 105 |
Archimedeanism | 114 |
Chapter XI | 117 |
Translating Temporal to Atemporal IS | 24 |
Temporally Definite and Indefinite Statements | 25 |
The Implicit Ubiquity of Now in Tensed Statements | 26 |
Dates and PseudoDates | 27 |
Times of Assertion | 28 |
Two Styles of Chronology | 30 |
Chapter IV | 31 |
The Temporal Transparency of Now | 32 |
Temporal Homogeneity | 35 |
Axioms for the Logical Theory of Chronological Propositions | 37 |
Temporal and Topological Logic | 43 |
The Completeness and Decidability of R | 44 |
Chapter V | 50 |
Semantics for Tense Logic | 56 |
The Completeness of Kt | 63 |
Chapter XII | 125 |
Further Definitions of Modality | 133 |
Chronological Purity | 144 |
The Absolute vs the Relative Conception of Time | 151 |
Some Applicable Distinctions | 159 |
Stochastic Processes and Branching Time | 166 |
Some Further Perspectives on Instantaneous World States | 173 |
The Concept of a World History | 179 |
and Temporal Determinism | 189 |
Temporal Determination | 203 |
A ManyValued Articulation of Temporal Logic | 216 |
Chapter XX | 234 |
Appendix I | 249 |
264 | |
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Palavras e frases frequentes
A. N. PRIOR A₁ application assertion assume assumption axiom schema axiomatization B₁ backwards linearity calculus Chapter characterize chronologically completeness proof concept condition consider construction context course of events D₁ define diagram DIODORUS CRONUS DS-system equivalent example finite follows formula future given Gp & Hp hence inference irreflexive issue machinery Martha Roosevelt Master Argument metric modal logic NICHOLAS RESCHER obtain occur p₁ position possible present proposition propositional logic provable pseudo-date Pẞ quantification theory quantifiers R-calculus R-operator R₁ R₂ raining in London realized RESCHER result rule of inference S₁ search tree specifically statement t-expressible t-structures t-valid t₁ t₂ tableau rules temporal logic temporal modalities temporally definite tense logic tense operators tense-logical tense-structure theorem theory thesis tion topological logic transition true truth truth-value U-relation Ut't valid variables