2024/09/13 by Shawn Standefer, Standefer, Shawn, Shay Allen Logan +3 · 1 citation
Computer Science · #Advanced Database Systems and Queries #Constraint Satisfaction and Optimization #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2409.08942
openalex publication_date 2024/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The family of relevant logics can be faceted by a hierarchy of increasingly fine-grained variable sharing properties -- requiring that in valid entailments A→ 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 BM (and that a related property of faithful lericone relevance holds of 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.