Metaconsistency of PM5M Relative to ZFC

Description:This appendix establishes the metaconsistency of the PM5M probabilistic–modal logic within the framework of ZFC (with standard measure theory and Kripke semantics). It demonstrates that if ZFC is consistent, then PM5M is also consistent. The work preserves conservativity on classical fragments, proves a collapse (reduction) result under memory-neutral conditions, and confirms that PM5M reduces to standard probabilistic modal logic when memory provides no additional information. The semantics of memory are formalized via finite-window aggregation with admissible weight vectors, ensuring alignment with the projective limit measure structure of Kolmogorov and Carathéodory.