Journal of Symbolic Logic 70 (3):993-1021 (2005)
| Abstract |
We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics as K4, S4, S4.1, K4.3, GL, or Grz are undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4,K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, if
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| DOI | 10.2178/jsl/1122038925 |
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References found in this work BETA
Reasoning About Knowledge.Ronald Fagin, Joseph Y. Halpern, Yoram Moses & Moshe Vardi - 1995 - MIT Press.
Two-Dimensional Modal Logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.
Products of Modal Logics, Part 1.D. Gabbay & V. Shehtman - 1998 - Logic Journal of the IGPL 6 (1):73-146.
Dynamic Topological Logic.Philip Kremer & Grigori Mints - 2005 - Annals of Pure and Applied Logic 131 (1-3):133-158.
Reduction of Second‐Order Logic to Modal Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):107-114.
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Citations of this work BETA
Multimo Dal Logics of Products of Topologies.Johan van Benthem, Guram Bezhanishvili, Balder ten Cate & Darko Sarenac - 2006 - Studia Logica 84 (3):369-392.
Multimo Dal Logics of Products of Topologies.J. Van Benthem, G. Bezhanishvili, B. Ten Cate & D. Sarenac - 2006 - Studia Logica 84 (3):369 - 392.
Multimo Dal Logics of Products of Topologies.J. van Benthem, G. Bezhanishvili, B. ten Cate & D. Sarenac - 2006 - Studia Logica 84 (3):369-392.
Non-Primitive Recursive Decidability of Products of Modal Logics with Expanding Domains.David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2006 - Annals of Pure and Applied Logic 142 (1):245-268.
On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
View all 11 citations / Add more citations
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