PM5M MVP — Probabilistic–Modal Logic with Memory: Minimal Working Prototype
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2025
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| _version_ | 1866902335976898560 |
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| author | Nikitin Leonid Vladimirovich, Nikitin Leonid Vladimirovich |
| author_facet | Nikitin Leonid Vladimirovich, Nikitin Leonid Vladimirovich |
| contents | <p><strong>Description:</strong><br>This package contains the reference minimal working prototype (MVP) of <strong>PM5M</strong>, 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.</p> <p>The logic is proven <strong>metaconsistent relative to ZFC</strong> (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.</p> <p><strong>Included in this release:</strong></p> <ul> <li> <p><strong>Core Python implementation</strong> (<code>pm5m_mvp.py</code>) of the PM5M formal system.</p> </li> <li> <p><strong>Example scenarios</strong> (<code>example_scenarios.json</code>) illustrating memory effects.</p> </li> <li> <p><strong>Comparative charts</strong> (<code>compare_soft.png</code>, <code>compare_medium.png</code>, <code>compare_strong.png</code>) showing PM5M behavior versus classical probability.</p> </li> <li> <p><strong>Google Colab snippet</strong> (<code>demo_colab_snippet.txt</code>) for immediate testing.</p> </li> <li> <p><strong>README</strong> with theoretical and usage notes.</p> </li> </ul> <p>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.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16785390 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | PM5M MVP — Probabilistic–Modal Logic with Memory: Minimal Working Prototype Nikitin Leonid Vladimirovich, Nikitin Leonid Vladimirovich Probability theory Modal logic Dependent events Covariance decay Memory effects Kochen–Stone theorem Asymptotic probability <p><strong>Description:</strong><br>This package contains the reference minimal working prototype (MVP) of <strong>PM5M</strong>, 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.</p> <p>The logic is proven <strong>metaconsistent relative to ZFC</strong> (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.</p> <p><strong>Included in this release:</strong></p> <ul> <li> <p><strong>Core Python implementation</strong> (<code>pm5m_mvp.py</code>) of the PM5M formal system.</p> </li> <li> <p><strong>Example scenarios</strong> (<code>example_scenarios.json</code>) illustrating memory effects.</p> </li> <li> <p><strong>Comparative charts</strong> (<code>compare_soft.png</code>, <code>compare_medium.png</code>, <code>compare_strong.png</code>) showing PM5M behavior versus classical probability.</p> </li> <li> <p><strong>Google Colab snippet</strong> (<code>demo_colab_snippet.txt</code>) for immediate testing.</p> </li> <li> <p><strong>README</strong> with theoretical and usage notes.</p> </li> </ul> <p>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.</p> |
| title | PM5M MVP — Probabilistic–Modal Logic with Memory: Minimal Working Prototype |
| topic | Probability theory Modal logic Dependent events Covariance decay Memory effects Kochen–Stone theorem Asymptotic probability |
| url | https://doi.org/10.5281/zenodo.16785390 |