论文标题
从接触关系到模态操作员，然后返回
From contact relations to modal operators, and back
论文作者
论文摘要
布尔触点代数的标准公理之一说，如果区域X与Y和Z的连接接触，则X与两个区域中的至少一个接触。我们的目的是检查该公理的更强大版本，如果X与某些区域的最高属于X接触，那么S中有一个与X接触的Y。我们研究了一个模态可能性操作员，该操作员在上述公理存在下在完全代数中可以定义，我们证明满足公理的完整代数类别与模态KTB-Elgebras类别密切相关。我们还证明，在完整的伸展接触代数的类别中，公理等同于陈述：每个区域都是隔离的。最后，我们在所谓的分辨率触点代数的类别中对模态运算符的解释进行了解释。
One of the standard axioms for Boolean Contact Algebras says that if a region x is in contact with the join of y and z, then x is in contact with at least one of the two regions. Our intention is to examine a stronger version of this axiom according to which if x is in contact with the supremum of some family S of regions, then there is a y in S that is in contact with x. We study a modal possibility operator which is definable in complete algebras in the presence of the aforementioned axiom, and we prove that the class of complete algebras satisfying the axiom is closely related to the class of modal KTB-algebras. We also demonstrate that in the class of complete extensional contact algebras the axiom is equivalent to the statement: every region is isolated. Finally, we present an interpretation of the modal operator in the class of the so-called resolution contact algebras.
