BK-lattices. Algebraic Semantics for Belnapian Modal Logics

BK-lattices. Algebraic Semantics for Belnapian Modal Logics
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BK-格子。

DOI：
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发表时间：
2012
期刊：
Studia Logica: An International Journal for Symbolic Logic
影响因子：
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通讯作者：
E. Latkin
E. Latkin
中科院分区：
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文献类型：
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作者：
S. Odintsov;E. Latkin

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早期的贝尔纳潘模态逻辑的代数语义是根据模态代数上的扭结构定义的。本文引入了BK-格类，证明了这类格与扭结构类的抽象闭包是一致的，并形成了一个簇。我们证明了BK-格的各种子簇的格是对偶同构的Belnapian模态逻辑BK的扩展格。最后，我们描述了不变量确定一个扭结构的模态代数。
Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK-lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK-lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK. Finally, we describe invariants determining a twist-structure over a modal algebra.