Abstract
The forward convergence constraint is important to time analysis. Without it, given two future moments to the same point, the time branches. This is unacceptable if one assumes that time is linear. Nevertheless, one may wish to consider time-branching in order to discuss future possibilities. One can have both a linear order for the time and branching through the combination of the tense logic semantics with those of an alethic logic which allows the evaluation of the timelines of other possible worlds. In this paper, I give the semantics and the tableaux systems for some alethic-tense logics. I review one in which worlds differ on their time orders (MT), another in which they agree on the time order (MOT), a pair of conditional tense logics (\(CT, CT^+\)), and the first-order version of MT. A brief philosophical discussion arises from every system.
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Acknowledgements
I want to thank Graham Priest, who saw an early draft copy of this paper. I also want to thank my postgraduate advisor Max Fernández de Castro Tapia and my college Balam Hidalgo López, who read and commented on my work. I also want to thank Eduardo Vargas, who helped me with some translation details. Finally, thanks to two anonymous referees who made some observations that improved the first version of this paper.
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Sánchez Hernández, J.C. Tableaux for Some Modal-Tense Logics Graham Priest’s Fashion. Stud Logica 110, 745–784 (2022). https://doi.org/10.1007/s11225-021-09974-x
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DOI: https://doi.org/10.1007/s11225-021-09974-x