Probability of Logical Formulas and Mathematical Theorems

<p>Description: This work extends my previous study on logically probable sentences \cite{olszewski2024} by introducing a combinatorial measure m that quantifies the fraction of satisfying assignments of logical formulas. Using Herbrand-style projections and propositional CNFs, we explore patterns, asymptotic behaviors, and zero-one laws in product algebras. The measure provides a new quantitative perspective on axioms, schemas, and proof complexity, offering insights for experimental meta-logic and SAT/SMT analysis. Note: This preprint is not peer-reviewed and may contain errors.</p>