Shawn Standefer | Searcharxiv

arXiv2026

A Formal Framework for Noisy Runtime Verification

We introduce the logic EDMon---an epistemic dynamic logic meant to model monitorability concepts in noisy runtime verification. Its syntax and semantics are defined and explained and the connection between EDMon and monitorability and noisy runtime verification concepts is explored. We then demonstrate that EDMon is sufficient to capture many of the results in the noisy runtime verification literature and catalog its relation to nearby logics and describe a large class of its theorems.

cs.LO↗

arXiv2024

Topics, Non-Uniform Substitutions, and Variable Sharing

The family of relevant logics can be faceted by a hierarchy of increasingly fine-grained variable sharing properties -- requiring that in valid entailments $A\to B$, some atom must appear in both $A$ and $B$ with some additional condition (e.g., with the same sign or nested within the same number of conditionals). In this paper, we consider an incredibly strong variable sharing property of lericone relevance that takes into account the path of negations and conditionals in which an atom appears in the parse trees of the antecedent and consequent. We show that this property of lericone relevance holds of the relevant logic $\mathbf{BM}$ (and that a related property of faithful lericone relevance holds of $\mathbf{B}$) and characterize the largest fragments of classical logic with these properties. Along the way, we consider the consequences for lericone relevance for the theory of subject-matter, for Logan's notion of hyperformalism, and for the very definition of a relevant logic itself.

math.LO↗