PLP-theory.docx

This paper introduces a novel framework called Pragmatic Logic of Proofs, a formal system designed to address uncertainties and meaningless statements, also through a pragmatic lens. Building on modal logic, the system incorporates new values—Meaninglessness, Uncertainty, Pragmatic Truth, Pragmatic Falsehood, and Pragmatic Neutrality. He introduces three modal operators: "can be proven", "can be refuted", "proven", "refuted", along with the classical modals "harmful", "helpful", "neutral". The logic extends the semantic structure of classical and modal systems by linking epistemic effectiveness with pragmatic evaluation. Statements that are useful are pragmatically true, those that are harmful are pragmatically false, and those that are neutral are pragmatically meaningless. The paper formalizes the interaction between epistemic properties (e.g., provability and refutability) and their pragmatic interpretations, providing axioms, inference rules, and truth tables. Applications of this logic are discussed in contexts requiring a balance between epistemic validity and practical consequences, such as decision-making, philosophy of science, and artificial intelligence. The framework also lays a foundation for exploring how theoretical and practical considerations influence logical reasoning.