Products of modal logics. Part 2: Relativised quantifiers in classical logic
Products of modal logics. Part 2: Relativised quantifiers in classical logic
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模态逻辑的产物。
DOI：
10.1093/jigpal/8.2.165
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
V. Shehtman
中科院分区：
文献类型：
--
作者：
D. Gabbay;V. Shehtman
在本文的第一部分，我们介绍了模式逻辑的产品，并证明了它们的公理化和f.m.p的基本结果。在本文中，我们证明了一个更强的结果--乘积f.m.p。模式逻辑的乘积，其中一些模式式是自反式或串联式的。这一定理被应用于经典一阶逻辑；我们发现了经典逻辑的一个新的平方片断(SF)，其中基本谓词是二进制的，所有量词都是相对化的，我们给出了它的f.m.p。在古典意义上。我们还证明了SF不包含在保护片段(和填充片段)中，并且它可以嵌入到关系代数的方程式理论中。1
In the rst part of this paper we introduced products of modal logics and proved basic results on their axiomatisability and the f.m.p. In this continuation paper we prove a stronger result - the product f.m.p. holds for products of modal logics in which some of the modalities are reflexive or serial. This theorem is applied in classical rst-order logic; we identify a new Square Fragment (SF) of the classical logic, where the basic predicates are binary and all quantiers are relativised, and for which we show the f.m.p. in the classical sense. Also we prove that SF not included in Guarded Fragment (and in Packed Fragment) and that it can be embedded into the equational theory of relation algebras. 1