Year: 2015
Type: article
Abstract: We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic flows, diagrams that trace structural changes through a proof but ignore logical information. As results we obtain a polynomial simulation of versions of Resolution, along with some extensions. We also show that these systems, as well as bounded-depth Frege systems, cannot polynomially simulate KS, by giving polynomial-size proofs of certain variants of the propositional pigeonhole principle in KS.
Author: Anupam Das
Institution: École Normale Supérieure de Lyon
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W1546322673