切触并-半格
Contact join-semilattices
摘要：
切触代数是基于区域的空间理论的主要工具之一。在\cite{dmvw1, dmvw2,iv,i1}中，通过删除布尔补运算将其推广。此外，我们还可以通过去掉运算meet来推广切触代数。因此，我们得到的结构，称为接触并半格（CJS）和结构，称为分配接触并半格（DCJS）。我们得到了CJS的集合论表示定理和DCJS的关系表示定理。作为推论，我们也得到拓扑表示定理。我们证明了CJS和DCJS的泛理论是相同的，是可判定的。
英文摘要：
Contact algebra is one of the main tools in region-based theory of space. In \cite{dmvw1, dmvw2,iv,i1} it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the operation meet. Thus we obtain structures, called contact join-semilattices (CJS) and structures, called distributive contact join-semilattices (DCJS). We obtain a set-theoretical representation theorem for CJS and a relational representation theorem for DCJS. As corollaries we get also topological representation theorems. We prove that the universal theory of CJS and of DCJS is the same and is decidable.
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