| Frank Wolter. Tense logic without tense operators. Mathematical Logic Quarterly, 42:145--171, 1996. |
.... i in a natural way as Kripke frames for this language. Now we can distinguish the theory of the reals from the theory of the rational numbers. Call a gap in a linearly ordered set hA; i a pair of open intervals B and C such that B C = and B [ C = A. It has been observed by Frank Wolter in [20] that the property of not possessing a gap can be expressed axiomatically in tense logic. It amounts to the property of not containing the linear re exive frame with two points. So, the tense logic of the real line is a splitting of the theory of dense linear orders without end points by a two ....
Frank Wolter. Tense logic without tense operators. Mathematical Logic Quarterly, 42:145 - 171, 1996.
....of the present paper is rather surprising. On our way to this theorem we shall establish some results which are of independent interest: Firstly we deliver axiomatizations by means of canonical formulas which are similar to those introduced in [12] for logics containing K4 and those introduced in [11] for tense logics. Then we prove completeness of all quasi normal subframe logics containing CSM 0 with respect to rather simple (descriptive) frames. Acknowledgements. I should like to thank M. Zakharyaschev and an anonymous referee for various helpful remarks on this paper. 2 Preliminaries ....
Wolter F.: Tense Logic without Tense operators. Mathematical Logic Quarterly 42, 145 - 171 (1996)
....already. Conversely, the following algorithm is in NExpTime: given , compute (in exponential time) and check whether is satis able in K. o This Theorem applies to e.g. i) the class of all strict linear orderings, ii) fhN; ig, iii) fhQ; ig, and (iv) fhR; ig, see [24, 29]. ....
F. Wolter. Tense logics without tense operators. Mathematical Logic Quarterly, 42:145-171, 1996.
....already. Conversely, the following algorithm is in NExpTime: given compute oe (in exponential time) and check whether oe is satisfiable in K. o This Theorem applies to e.g. i) the class of all strict linear orderings, ii) fhN; ig, iii) fhQ; ig, and (iv) fhR; ig, see [24, 29]. ....
F. Wolter. Tense logics without tense operators. Mathematical Logic Quarterly, 42:145--171, 1996.
....NExpTime hard already. Conversely, the following algorithm is in NExpTime: given , compute (in exponential time) and check whether is satis able in K. o This Theorem applies to e.g. i) the class of all strict linear orderings, ii) fhN; ig, iii) fhQ; ig, and (iv) fhR; ig, see [25, 30]. ....
F. Wolter. Tense logics without tense operators. Mathematical Logic Quarterly, 42:145-171, 1996.
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Frank Wolter. Tense logic without tense operators. Mathematical Logic Quarterly, 42:145--171, 1996.
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