An Algebraic Approach to Subframe Logics. Modal Case
An Algebraic Approach to Subframe Logics. Modal Case
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子帧逻辑的代数方法。
DOI：
10.1215/00294527-1306190
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Jibladze
中科院分区：
文献类型：
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作者：
G. Bezhanishvili;S. Ghilardi;M. Jibladze
证明了如果模态公式在wk4 -代数（B, 2）上被驳倒，那么它在与（B, 2）的相对性的子代数同构的有限wk4 -代数上被驳倒。作为一个直接的结果，我们得到了wK4上的每个子帧和协子帧逻辑具有有限模型属性。一方面，给出了Fine[11]和Zakharyaschev[22]对K4的结果的纯代数证明。另一方面，将Fine-Zakharyaschev结果推广到wK4。
We prove that if a modal formula is refuted on a wK4-algebra (B, 2), then it is refuted on a finite wK4-algebra which is isomorphic to a subalgebra of a relativization of (B, 2). 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 [11] and Zakharyaschev [22] for K4. On the other hand, it extends the Fine-Zakharyaschev results to wK4.