Abstract
In this section and the next we shall investigate tense logics which are based on quantificational logics. The first of these bases, called Q, is the classical theory of quantification. The others, Q* and QQ**, are free quantification theories which permit some of the individual constants (= free individual variables) to be non-designating.1
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Notes
More about free quantification theory can be had from Leblanc, 1976.
Infinite stocks of individual variables, individual constants, and, for each m, m-place predicates are assumed here.
0-place predicates play the role of statement letters.
See McArthur and Leblanc, 1975 for illustrations.
But the set is satisfiable on model-theoretic semantics. For complete details on this matter see Leblanc, 1976.
The Q-systems are based on those developed by Kripke (see Kripke, 1963) and Leblanc (see Leblanc, 1971) for quantificational modal logics. QCL* is equivalent to the free, quantificational tense logic pioneered by Cocchiarella in 1966.
Q3*a and Q3*b, as well as T37 and T38 are somewhat redundant as axioms of QKt * They turn out to be provable with restrictions similar to that on Q5. However, given our semantics they are valid in their unrestricted forms and must be counted as axioms.
These truth conditions are similar to those used by Hughes and Cresswell for their version of QSâ Although they are not three-valued, they are similar to Bochvar three-valued semantics for classical logic. See Rescher, 1969, pp. 29-34.
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© 1976 Springer Science+Business Media Dordrecht
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McArthur, R.P. (1976). Quantificational Tense Logics. In: Tense Logic. Synthese Library, vol 111. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3219-2_4
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DOI: https://doi.org/10.1007/978-94-017-3219-2_4
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