We develop a semantic rate-distortion theory for reversible logging under a closure-preserving fidelity criterion. An execution history is modeled as a finite set of logged facts, and rollback-relevant meaning is captured by a monotone semantic closure induced by an effective rule system such as Datalog. We introduce a bounded distortion that edits one logged fact and measures the resulting change in closure. A canonical deletion scan decomposes the log into an irredundant core and a redundant remainder; under admissible reconstructions, redundant facts become information-theoretically invisible, yielding a core-only rate-distortion reduction. At perfect fidelity, overlaps among zero-distortion reconstructions induce a confusability hypergraph that determines the minimum rate. We instantiate the framework on reversible causal nets and reversible prime event structures under multiple reversing disciplines, and validate the predictions numerically.

翻译：我们发展了一种闭包保持保真度准则下可逆日志记录的语义率失真理论。执行历史被建模为有限个已记录事实的集合，回滚相关的语义由有效规则系统（如Datalog）诱导的单调语义闭包捕获。我们引入一种有界失真，对单个被记录事实进行编辑，并测量闭包在编辑后的变化量。通过典范删除扫描，日志被分解为无冗余核心和冗余剩余部分；在允许的重构下，冗余事实在信息论意义上变得不可见，从而得到仅基于核心的率失真约简。在完美保真度下，零失真重构之间的重叠构成了一个混淆超图，该超图决定了最小率。我们将该框架实例化于可逆因果网络和多种回滚原则下的可逆素数事件结构，并通过数值实验验证了相关预测。