On the Construction of S4M3 Modal Coupling System, Operator Innovation and Investigation of Mesoscopic Information Theory Paradigm

Classical S4 modal logic is established on Boolean distributive algebras and can only characterize binary deterministic states, lacking the ability to describe intermediate informational states with mere possibility without necessity. Traditional quantum logic constructs propositional algebra based on orthomodular lattices but lacks native modal operators to distinguish necessity and possibility. Most existing modal extensions of orthomodular lattices retain the classical K axiom, which is incompatible with non-distributive lattice structures and fails to establish an independent mesoscopic information framework. To solve these defects, this paper constructs the S4M3 modal coupling system, which structurally integrates the S4 modal paradigm with the M3 diamond orthocomplemented modular lattice. It replaces the classical modal K axiom with an original composite B3 axiom system, abandons Kripke possible-world semantics, and adopts Tarskian algebraic semantics to realize intrinsic algebraic definition of modal operators. This paper originally proposes the Liu Pole critical concept and the R-space topological conjecture, defines the mesoscopic modal correlation saturation threshold 1+√2, and establishes the exclusive mesoscopic information unit mobit. It completes the non-physical modal reinterpretation of CHSH-type correlation and Leggett-Garg inequalities, verifying that quantum correlation anomalies can be pure logical inferences of mesoscopic modal states of affairs. The results show that the S4M3 coupling operator breaks the inherent limitation that classical S4 algebra must rely on distributive lattices, realizing the compatible unification of non-distributive modular lattices and S4 modal characteristics. The mesoscopic domain is not a physical scale concept but an independent state category at the modal level. Completely different from Wu Hun’s material ontology of information and Floridi’s data-semantic information theory, this study extends the Shao-Yong–Leibniz–Boole (SLB) programme and constructs a novel mesoscopic information philosophy paradigm based on Russell’s neutral monism, providing rigorous mathematical and philosophical support for modal logic expansion, fundamental interpretation of quantum correlation, and mesoscopic information modeling.