Beyond the Syllogism: A Formal State-Transition Logic for Complex Systems

This paper proposes a radical alternative to classical Aristotelian logic for describing complex systems. The classical syllogism (A→B;B→C∴A→CA→B;B→C∴A→C) assumes an unobstructed flow of inference. However, it fails to account for systemic resistance, temporal constraints, and the neuro-energetic cost of action. In medicine, law, industry, and military science, we frequently encounter a paradox: a subject possesses complete declarative knowledge (the "map") but fails to execute the required action. We introduce State-Transition Logic (STL), a formal apparatus that replaces static categorical deduction with dynamic transition operators. The core formula of action is defined as Dc>RDc>R, where DcDc represents Dispositional Commitment (the stable readiness to act) and RR represents Systemic Resistance (the sum of internal and external friction). The paper demonstrates the universal applicability of STL across four domains: post-stroke apathy in neurology, human error in industrial production, functional responsibility in jurisprudence, and command execution in military science. Conceptual Framework: Triadic Theory of Action / PM vs Dc (Sanzhiev, 2026).