Logica Universalis 8 (3-4):407-422 (2014)

Marcelo E. Coniglio
University of Campinas
In 1940 Dugundji proved that no system between S1 and S5 can be characterized by finite matrices. Dugundji’s result forced the development of alternative semantics, in particular Kripke’s relational semantics. The success of this semantics allowed the creation of a huge family of modal systems. With few adaptations, this semantics can characterize almost the totality of the modal systems developed in the last five decades. This semantics however has some limits. Two results of incompleteness showed that not every modal logic can be characterized by Kripke frames. Besides, the creation of non-classical modal logics puts the problem of characterization of finite matrices very far away from the original scope of Dugundji’s result. In this sense, we will show how to update Dugundji’s result in order to make precise the scope and the limits of many-valued matrices as semantic of modal systems. A brief comparison with the useful Chagrov and Zakharyaschev’s criterion of tabularity for modal logics is provided
Keywords Modal logics  matrix logics  Dugundji’s theorem
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DOI 10.1007/s11787-014-0106-4
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References found in this work BETA

New Foundations for Lewis Modal Systems.E. J. Lemmon - 1957 - Journal of Symbolic Logic 22 (2):176-186.
Extensions of the Lewis System S5.Schiller Joe Scroggs - 1951 - Journal of Symbolic Logic 16 (2):112-120.

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