The Logical Embedding of Universal Frame Logic: A Sequent Calculus and Classical Interpretation
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901637479530496 |
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| author | Kevin Fathi |
| author_facet | Kevin Fathi |
| contents | <p>Universal Frame Logic (UFL) is a formal language developed to express recursive<br>symbolic coherence across layered frames of interpretation. In this paper, we define a<br>precise syntax and sequent calculus for UFL, including frame-indexed formula typing,<br>entropy-annotated inference, and frame morphism dynamics.<br>We prove that UFL is a conservative extension of first-order logic: any UFLderivable<br>statement whose entropy is bounded and whose type is ground-resolvable<br>corresponds to a provable formula in classical logic. We construct a translation from<br>UFL derivations to standard first-order sequent derivations, preserving truth and evaluation under frame-lifting operations.<br>This establishes that the Batesonian framework of recursive coherence and symbolic<br>entropy — when precisely formalized — is logically sound, semantically complete, and classically interpretable.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15204710 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Logical Embedding of Universal Frame Logic: A Sequent Calculus and Classical Interpretation Kevin Fathi Universal Frame Logic Recursive Type Arithmetic Sequent Calculus Logical Embedding Formal Systems Mathematical Logic Conservativity First-Order Logic Typed Logic Multi-Sorted Logic Symbolic Entropy Frame Semantics Model Theory Recursive Proof Systems Frame Morphisms Completeness Theorem Logical Soundness Typed Sequent Derivation Batesonian Logic Formal Deduction <p>Universal Frame Logic (UFL) is a formal language developed to express recursive<br>symbolic coherence across layered frames of interpretation. In this paper, we define a<br>precise syntax and sequent calculus for UFL, including frame-indexed formula typing,<br>entropy-annotated inference, and frame morphism dynamics.<br>We prove that UFL is a conservative extension of first-order logic: any UFLderivable<br>statement whose entropy is bounded and whose type is ground-resolvable<br>corresponds to a provable formula in classical logic. We construct a translation from<br>UFL derivations to standard first-order sequent derivations, preserving truth and evaluation under frame-lifting operations.<br>This establishes that the Batesonian framework of recursive coherence and symbolic<br>entropy — when precisely formalized — is logically sound, semantically complete, and classically interpretable.</p> |
| title | The Logical Embedding of Universal Frame Logic: A Sequent Calculus and Classical Interpretation |
| topic | Universal Frame Logic Recursive Type Arithmetic Sequent Calculus Logical Embedding Formal Systems Mathematical Logic Conservativity First-Order Logic Typed Logic Multi-Sorted Logic Symbolic Entropy Frame Semantics Model Theory Recursive Proof Systems Frame Morphisms Completeness Theorem Logical Soundness Typed Sequent Derivation Batesonian Logic Formal Deduction |
| url | https://doi.org/10.5281/zenodo.15204710 |