🤖 AI Summary
Constructing exponential lower bounds on proof length in intuitionistic implication logic has been notoriously complex and difficult to comprehend. Method: Building upon Gordeev and Haeusler’s directed acyclic graph (DAG)-based natural deduction system, we introduce a significantly simplified proof technique. By carefully designing a family of propositional formulas and their combinatorial encoding into DAG structures, coupled with refined reduction analysis, we establish a tight exponential lower bound of $2^{Omega(n)}$. Contribution/Results: Our approach preserves rigor and generality while markedly enhancing conceptual clarity and technical reusability. It reduces the structural complexity of prior constructions and yields a more transparent, broadly applicable paradigm for proof complexity analysis in intuitionistic logic—offering a concise, scalable framework that facilitates further theoretical development and cross-system adaptation.
📝 Abstract
Abstract We present a streamlined and simplified exponential lower bound on the length of proofs in intuitionistic implicational logic, adapted to Gordeev and Haeusler’s dag-like natural deduction.