## Temporal Logic: From Ancient Ideas to Artificial IntelligenceTemporal Logic: From Ancient Ideas to Artificial Intelligence deals with the history of temporal logic as well as the crucial systematic questions within the field. The book studies the rich contributions from ancient and medieval philosophy up to the downfall of temporal logic in the Renaissance. The modern rediscovery of the subject, which is especially due to the work of A. N. Prior, is described, leading into a thorough discussion of the use of temporal logic in computer science and the understanding of natural language. Temporal Logic: From Ancient Ideas to Artificial Intelligence thus interweaves linguistic, philosophical and computational aspects into an informative and inspiring whole. |

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### Contents

PART 1 TIME AND LOGIC FROM SYNTHESIS TO DISSOCIATION | 6 |

11 The Seafight Tomorrow | 10 |

Diodorus Cronus | 15 |

13 The Study of Tenses in the Middle Ages | 33 |

14 Temporal Ampliation | 39 |

15 The Duration of the Present | 43 |

16 The Logic of Beginning and Ending | 52 |

17 Time and Consequents | 65 |

27 Tense Logic and Special Relativity | 197 |

28 Some Basic Systems of Temporal Logic | 203 |

29 Four Grades of TenseLogical Involvement | 216 |

210 Metric Tense Logic | 231 |

Temporal Logic | 241 |

31 Two Paradigms of Temporal Logic | 243 |

32 Indeterministic Tense Logic | 257 |

33 Leibnizian Tense Logic | 270 |

18 Temporalis the Logic of WHILE | 71 |

Divine Foreknowledge | 87 |

110 The Downfall of Medieval Tenselogic | 109 |

111 Logic as a Timeless Science | 114 |

Part 2 Time and Logic Reunited | 118 |

21 The 19th century and Boolean logic | 122 |

Time and Modality | 128 |

to Temporal logic | 149 |

24 A ThreePoint Structure of Tenses | 155 |

25 AN Priors Tenselogic | 167 |

26 The Idea of Branching Time | 180 |

34 Tense Logic and Counterfactual Reasoning | 282 |

35 Logic of Durations | 303 |

36 Graphs for Time and Modality | 320 |

37 Temporal Logic and Computer Science | 344 |

4 Conclusion | 366 |

Appendix | 373 |

386 | |

405 | |

Some Important Logicians and Philosophers | 413 |

### Common terms and phrases

A-concepts A. N. Prior According analysis Anselm antecedent argued Aristotle assume assumption axioms B-logic B-theory before(a,b,x Borges branching Buridan causal chapter CIMP computer science concept conceptual graphs consequence consequentia considered contingent future corresponding counterfactual crucial defined definition Diodorus discussion durations equivalent example existential graphs fact false formulated Hamblin history of logic idea implication instant propositions interpretation ISBN Jespersen Lavenham Leibniz logicians Lukasiewicz Master Argument means medieval logic medieval logicians metric tense logic modal logic natural language necessity notion obviously Ockham Ockhamistic operator past Peirce Peirce's Peircean philosophical predicate present Prior problem Proof provable proved question reason regarding Reichenbach rejected relation relevant rule Scholastic sea-fight semantics Socrates sophism statement Stephen Albert structure symbolic tempo-modal temporal logic temporal proposition temporalis tense logic tense-logical theorem theory thesis tomorrow true truth value unbroken cuts valid William of Ockham Yu Tsun

### Popular passages

Page 1 - What then is time? If no one asks me. I know; if I wish to explain it to one that asketh, I know not...

Page ii - University of Alberta Editorial Board JOHAN VAN BENTHEM, University of Amsterdam GREGORY N. CARLSON, University of Rochester DAVID DOWTY, Ohio State University, Columbus GERALD GAZDAR, University of Sussex, Brighton IRENE...