Four Equivalent Relations between MCP and CP and Its Implication in Quantum and Information Theory

Abstract

(Norraw) modal propositional logic (MCP) tries to be a strict model for quantum and information theory, but it has serious difficulties in syntax, semantics, and metaphysics. According to the guiding definition of minimal hidden variables, this study presents four equivalences between MCP and classical propositional logic (CP). It concludes that MCP is CP containing minimal syntactic hidden variables, modal axiom represents the classification of CP formulas, and possible world is CP formula as assignment background, which establishes a simpler and unified basis for quantum information theory. The black modal of classical propositional logic (BCP), as an assisted discovery method, reveals that modal nature is actually to express the interdependence between things and their environment in a mathematical way, which can express the holism, dialectics, and uncertainty of metaphysics, and use mark hiding (e.g., f (x) is a function of x, f () is the functional expression, functional-e for short, and “□” is, in fact, a cluster of functional-es in which superscript and subscript are hidden) that does not affect the effectiveness of reasoning to express a more simplified, efficient, and consistent artificial intelligence.