Equilibrium Logic: A Computable Three-Valued System for Self-Referential Undecidability
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| Sprache: | Englisch |
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2025
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| _version_ | 1866901697411940352 |
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| author | Mikhail, Vasilyev |
| author_facet | Mikhail, Vasilyev |
| contents | <h2>Abstract</h2> <p><strong>This paper introduces Three-Valued Equilibrium Logic (3PEL)</strong> — a novel formal system that handles self-referential statements in a computable and paradox-free way. It avoids collapse into classical paradoxes like the Liar or Gödel’s sentence, while maintaining deductive integrity and semantic clarity.</p> <h3>Key Features</h3> <p> Defines a new third truth value: <strong>E (Equilibrium)</strong> — a computable form of structural undecidability.<br> Built on partial order semantics and monotonic connectives.<br> Enables modeling of <strong>truth-tolerant self-reference</strong> without paradox.</p> <h3>Theoretical Contributions</h3> <p>✔️ Proves that <strong>3PEL is not reducible</strong> to Kleene K3, LP, or existing paraconsistent logics.<br>✔️ Demonstrates that the <strong>E-STATUS</strong> decision problem is <strong>decidable</strong> and lies in <strong>EXPTIME</strong>.<br>✔️ Allows formal reasoning about statements like “This formula is not provable” in a controlled, analyzable way.</p> <h3>Applications</h3> <p>This logic may be relevant to:</p> <ul> <li>AI safety and recursive reasoning systems</li> <li>Reflective theorem proving</li> <li>Non-classical verification tools</li> <li>Formal modeling of self-reference in machine learning systems</li> </ul> <p><strong>Author</strong>: Mikhail Vasilyev </p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16752118 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Equilibrium Logic: A Computable Three-Valued System for Self-Referential Undecidability Mikhail, Vasilyev equilibrium logic Three-valued logic Self-reference Undecidability Formal systems AI alignment Interpretability Meta-reasoning Computable logic Consistency without completeness Superintelligence Foundations of artificial general intelligence Logical uncertainty Liar paradox Gödelian limitations Computational semantics <h2>Abstract</h2> <p><strong>This paper introduces Three-Valued Equilibrium Logic (3PEL)</strong> — a novel formal system that handles self-referential statements in a computable and paradox-free way. It avoids collapse into classical paradoxes like the Liar or Gödel’s sentence, while maintaining deductive integrity and semantic clarity.</p> <h3>Key Features</h3> <p> Defines a new third truth value: <strong>E (Equilibrium)</strong> — a computable form of structural undecidability.<br> Built on partial order semantics and monotonic connectives.<br> Enables modeling of <strong>truth-tolerant self-reference</strong> without paradox.</p> <h3>Theoretical Contributions</h3> <p>✔️ Proves that <strong>3PEL is not reducible</strong> to Kleene K3, LP, or existing paraconsistent logics.<br>✔️ Demonstrates that the <strong>E-STATUS</strong> decision problem is <strong>decidable</strong> and lies in <strong>EXPTIME</strong>.<br>✔️ Allows formal reasoning about statements like “This formula is not provable” in a controlled, analyzable way.</p> <h3>Applications</h3> <p>This logic may be relevant to:</p> <ul> <li>AI safety and recursive reasoning systems</li> <li>Reflective theorem proving</li> <li>Non-classical verification tools</li> <li>Formal modeling of self-reference in machine learning systems</li> </ul> <p><strong>Author</strong>: Mikhail Vasilyev </p> |
| title | Equilibrium Logic: A Computable Three-Valued System for Self-Referential Undecidability |
| topic | equilibrium logic Three-valued logic Self-reference Undecidability Formal systems AI alignment Interpretability Meta-reasoning Computable logic Consistency without completeness Superintelligence Foundations of artificial general intelligence Logical uncertainty Liar paradox Gödelian limitations Computational semantics |
| url | https://doi.org/10.5281/zenodo.16752118 |