Abstract
Branching tense logics are simply described from the axiomatic perspective: they lack one, or both, of axioms A9 and A10. The reader will recall these schemata to have been singled out as ‘axioms of linearality’ in Chapter 2. But a more intuitive characterization is given in semantic terms: the temporal orders represented by such logics permit forks, or branches.
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Notes
See Prior, 1967, Appendix A.
Rescher and Urquhart, 1971, Chapter 4.
Specifically, as in the Special Theory of Relativity. On this point see Rennie, 1969 and Lucas, 1971.
A more detailed interpretation of Kb along these lines is found in Rescher and Urquhart, 1971, Chapter 4.
This observation is Prior’s. See Prior, 1967, p. 133.
The standard work on Stoic logic is Mates, 1952. These definitions are Prior’s.
Although I have reproduced Prior’s findings on the question, recent developments suggest that at least one of the entries in this table is incorrect. Rescher and Urquhart report that the Aristotelian fragment of CR and Kb is somewhat stronger than B, but is not S, They leave the nature of the system an open question.
See Prior, 1967, Chapter 7, especially pp. 122-127. In addition Thomason, 1970a bears on the semantic formulation here given for OT. Also consult Vaughn McKim and Charles Davis, Temporal Modalities and the Future, Notre Dame Journal of Formal Logic (April 1976 ), pp. 233 - 238.
‘O’ for Ockham, whose views on future contingency inspired this approach. Also see McArthur, 1975.
These are often called maximal R-chains in E2.
A similar distinction between pure future statements (for which A20 does not hold) and others (for which it does) is made by Ockham. See McArthur, 1975.
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© 1976 Springer Science+Business Media Dordrecht
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McArthur, R.P. (1976). Branching Tense Logic and Temporal Modality. In: Tense Logic. Synthese Library, vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3219-2_3
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DOI: https://doi.org/10.1007/978-94-017-3219-2_3
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