@BOOK{prior67:_past_presen_futur,
title = {Past, Present and Future},
publisher = {Oxford University Press},
year = {1967},
author = {A. Prior},
abstract = {
This book gives a full account of the more informal aspect of symbolic
tense-logic up to the time of writing, work which the author originated
and has led in the last 15 years. Considerable reference is made
to studies of time and tenses in previous logic, classical, medieval,
and recent. A wide variety of calculi are introduced to investigate
various problems. Fundamental technical problems, such as completeness
proofs, are not dwelt on, but a fair amount of formal work is done.
Chapter I reviews informal logic of tenses, particularly McTaggart
on past-present-future and earlier-later. Chapter II reviews the
solved problem of formalising Diodorean modality. Chapter III introduces
two of the four main approaches to symbolising tense-logic: the calculi
in the tense operators $P,G,H,F$ ("It has been the case that...",
etc.), and the calculi in the relation $U$ between instants, within
which $P,G,H,F$ can be handled. These calculi have intended interpretations
in terms of time. Here and in Chapter IV the particular calculi corresponding
to particular assumptions about time are discussed. (The relevant
formal results of Cocchiarella, Lemmon and Scott, etc., are summarised
in an appendix.) Chapter V is about the logic of "world-states".
In Chapter VI the third main approach, metric tense-logic with operators
such as $Fn$ ("It will be the case after an interval $n$ that..."),
is introduced, and tentative postulates put forward. In Chapter VII
determinism is discussed. A modal operator $L$ for "It is now-unpreventably
the case that..." is introduced, and asymmetry between past-tense
and future-tense expressions is set up. This is done in two ways,
corresponding to two counters to Diodorus' "master argument". Intended
interpretations in terms of branching time are given. Chapter VIII
looks at the extending of tense-logic to include predicates and individual
quantifiers, and the difficulties that arise.
This book is a thorough survey of a field of symbolic logic of growing
importance; it will be stimulating to those working with either traditional
problems or contemporary mathematical techniques in logic. }
}