Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

An Analytic Propositional Proof System On Graphs

Matteo Acclavio 1 Ross Horne 1 Lutz Straßburger 2
2 PARTOUT - Automatisation et ReprésenTation: fOndation du calcUl et de la déducTion
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary (undirected) graphs. This means that we lose the tree structure of the formulas corresponding to the cographs, and we can no longer use standard proof theoretical methods that depend on that tree structure. In order to overcome this difficulty, we use a modular decomposition of graphs and some techniques from deep inference where inference rules do not rely on the main connective of a formula. For our proof system we show the admissibility of cut and a generalization of the splitting property. Finally, we show that our system is a conservative extension of multiplicative linear logic with mix, and we argue that our graphs form a notion of generalized connective.
Document type :
Preprints, Working Papers, ...
Complete list of metadata
Contributor : Lutz Straßburger Connect in order to contact the contributor
Submitted on : Wednesday, December 23, 2020 - 6:32:51 PM
Last modification on : Thursday, January 20, 2022 - 5:30:08 PM


Files produced by the author(s)


  • HAL Id : hal-03087392, version 1


Matteo Acclavio, Ross Horne, Lutz Straßburger. An Analytic Propositional Proof System On Graphs. 2020. ⟨hal-03087392⟩



Les métriques sont temporairement indisponibles