2002/11/05 by Kosta Došen, Dosen, K., Zoran Petrić +1
Computer Science · #03F07 #03G30 #16G99 #18A15 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.math/0211090
openalex publication_date 2002/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation iff they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. This paper examines in the setting of categorial proof theory the conjecture that two derivations with the same premises and conclusions stand for the same proof iff they have the same generality. For that purpose generality is defined within a category whose arrows are equivalence relations on finite ordinals, where composition is rather complicated. Several examples are given of deductive systems of derivations covering fragments of logic, with the associated map into the category of equivalence relations of generality. This category is isomorphically represented in the category whose arrows are binary relations between finite ordinals, where composition is the usual simple composition of relations. This representation is related to a classical representation result of Richard Brauer.