2026-07-26T02:32:22Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22796 2025-02-03T10:18:31Z ddc:004 open_access

A Strictly Linear Subatomic Proof System Barrett, Victoria Guglielmi, Alessio Ralph, Benjamin Deep inference Open deduction Subatomic logic Decision trees Explicit substitutions Cut elimination Proof theory We present a subatomic deep-inference proof system for a conservative extension of propositional classical logic with decision trees that is strictly linear. In a strictly linear subatomic system, a single linear rule shape subsumes not only the structural rules, such as contraction and weakening, but also the unit equality rules. An interpretation map from subatomic logic to propositional classical logic recovers the usual semantics and proof theoretic properties. By using explicit substitutions that indicate the substitution of one derivation into another, we are able to show that the unit-equality inference steps can be eliminated from a subatomic system for propositional classical logic with only a polynomial complexity cost in the size of the derivation, from which it follows that the system p-simulates Frege systems, and we show cut elimination for the resulting strictly linear system. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Victoria Barrett and Alessio Guglielmi and Benjamin Ralph 2025 Is Part Of LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2025.39 urn:nbn:de:0030-drops-227967 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.39 eng https://creativecommons.org/licenses/by/4.0/legalcode