We prove that if a modal formula is refuted on a wK4-algebra, then it is refuted on a finite wK4-algebra A which is isomorphic to a subalgebra of a relativization of A. As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4. On the other hand, it extends the Fine-Zakharyaschev results to wK4.
An algebraic approach to subframe logics. Modal case / G. Bezhanishvili, S. Ghilardi, M. Jibladze. - In: NOTRE DAME JOURNAL OF FORMAL LOGIC. - ISSN 0029-4527. - 52:2(2011), pp. 187-202.
An algebraic approach to subframe logics. Modal case
S. GhilardiSecondo
;
2011
Abstract
We prove that if a modal formula is refuted on a wK4-algebra, then it is refuted on a finite wK4-algebra A which is isomorphic to a subalgebra of a relativization of A. As an immediate consequence, we obtain that each subframe and cofinal subframe logic over wK4 has the finite model property. On the one hand, this provides a purely algebraic proof of the results of Fine and Zakharyaschev for K4. On the other hand, it extends the Fine-Zakharyaschev results to wK4.
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