Abstract
In Kripke’s original papers on modal logic semantic tableaus were used extensively. But they were quite different from the ones we have been investigating. Instead of “updating” a branch, a new alternate tableau was created. This in turn could give rise to other alternate tableaus, and so on. The final proof was often more of a forest than a single tree. The disadvantages of such an approach include, of course, complexity. On the other hand, there are certain clear advantages. Branch updating techniques of the sort we have been using cause one to forget the past. Thus they are less than ideal for logics in which you can go home again, logics like B for example. They are also inappropriate for first order constant domain logics in which, so to speak, the discovery that something exists in an alternate world makes one realize it must have existed in the world we left behind. Keeping track of all the various alternate tableaus avoids these problems, since there is then have the potential for interaction.
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© 1983 Springer Science+Business Media Dordrecht
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Fitting, M. (1983). Prefixed Tableau Systems. In: Proof Methods for Modal and Intuitionistic Logics. Synthese Library, vol 169. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2794-5_9
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DOI: https://doi.org/10.1007/978-94-017-2794-5_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8381-4
Online ISBN: 978-94-017-2794-5
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