In \cite{sp25}, continuous information frames were introduced that capture exactly all continuous domains. They are obtained from the information frames considered in \cite{sp21} by omitting the conservativity requirement. Information frames generalise Scott's information systems~\cite{sc82}: Instead of the global consistency predicate, there is now a local consistency predicate for each token. Strong information frames are obtained by strengthening the conditions for these predicates. Let $\CIF$ and $\SIF$ be the corresponding categories. In \cite{sxx08} another generalisation of Scott's information systems was introduced which also exactly captures all continuous domains. As shown in \cite{hzl15}, the definition can be simplified while maintaining the representation result. Let $\CIS$ and $\SCIS$ be the corresponding categories. It is shown that all these categories are equivalent. Moreover, the equivalence extends to the subcategories of (strong) continuous information frames with truth elements. Such information frames capture exactly all pointed continuous domains. Continuous information frames are families of rudimentary logics, associated with each token is a local consistency predicate and an entailment relation. However, they lack the expressive power of propositional logic. In an attempt to make each of this logics more expressible, continuous stratified conjunctive logics are introduced. These are families of conjunctive logics. The category $\CSL$ of such logics is shown to be isomorphic to $\SIF_{\bt}$, the category of strong continuous information frames with a truth element.

翻译：在文献\cite{sp25}中，引入了连续信息框架，它们精确刻画了所有连续论域。这些框架是通过省略文献\cite{sp21}中所考虑信息框架的保守性要求而得到的。信息框架推广了Scott的信息系统~\cite{sc82}：取代全局一致性谓词，现在每个令牌都有一个局部一致性谓词。通过强化这些谓词的条件，可以得到强信息框架。令$\CIF$和$\SIF$为对应的范畴。文献\cite{sxx08}中引入了Scott信息系统的另一种推广，它同样精确刻画了所有连续论域。如文献\cite{hzl15}所示，该定义可以在保持表示结果的前提下得到简化。令$\CIS$和$\SCIS$为对应的范畴。本文证明了所有这些范畴都是等价的。此外，该等价性可推广到具有真值元素的（强）连续信息框架子范畴。此类信息框架精确刻画了所有带基点的连续论域。连续信息框架是一族基本逻辑，每个令牌关联一个局部一致性谓词和一个蕴涵关系。然而，它们缺乏命题逻辑的表达能力。为了增强这些逻辑各自的表达能力，本文引入了连续分层合取逻辑。这是一族合取逻辑。证明了此类逻辑的范畴$\CSL$与带真值元素的强连续信息框架范畴$\SIF_{\bt}$同构。