PM5M MVP — Probabilistic–Modal Logic with Memory: Minimal Working Prototype

Description:This package contains the reference minimal working prototype (MVP) of PM5M, a probabilistic–modal logic with an explicit memory operator, formally introduced in Nikitin’s Theorems I & II. PM5M extends the Kolmogorov–Carathéodory probabilistic framework with finite-window memory aggregation, enabling reasoning about dependent events under modal constraints. The logic is proven metaconsistent relative to ZFC (with standard measure theory and Kripke semantics): if ZFC is consistent, PM5M is also consistent. It conservatively extends classical probability and modal logic, and reduces to the standard probabilistic modal logic when memory provides no additional information. Included in this release: Core Python implementation (pm5m_mvp.py) of the PM5M formal system. Example scenarios (example_scenarios.json) illustrating memory effects. Comparative charts (compare_soft.png, compare_medium.png, compare_strong.png) showing PM5M behavior versus classical probability. Google Colab snippet (demo_colab_snippet.txt) for immediate testing. README with theoretical and usage notes. This MVP demonstrates key PM5M constructs — probability saturation, forgetting operators, modal necessity/possibility with memory weights — and serves as a reference for reproducibility, experimentation, and further formal research.