Closure-Preserving Rate-Distortion for Reversible Logging

Abstract

We study semantic compression of reversible-execution evidence for rollback reasoning. A run is a finite fact base; rollback semantics are modeled by a monotone closure operator induced by function-free Horn rules. A single edit replaces one fact by another; fidelity is the Jaccard discrepancy of the resulting closures, yielding a finite-alphabet distortion for rate-distortion analysis. A deterministic deletion scan decomposes the log into an irredundant core--preserving the closure--and a redundant remainder. Under admissible reconstructions (facts entailed by the original log), redundant facts are distortion-invisible, reducing the semantic rate-distortion function to a core-only optimization scaled by the core probability mass. At zero distortion, the optimal rate is a hypergraph entropy induced by overlaps of zero-distortion reconstruction sets on the core. We introduce a rollback-task loss based on a rollback observable, deriving parallel endpoint and factorization laws. The framework is instantiated on reversible causal nets and discussed in the event-structure view, showing how reversing disciplines yield different cores and compression frontiers. Numerical evaluation uses Blahut-Arimoto to design single-letter test channels and Monte Carlo reconstruction to assess end-to-end degradation at the log level.