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| Autor principal: | |
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| Formato: | Recurso digital |
| Lenguaje: | inglés |
| Publicado: |
Zenodo
2025
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| Materias: | |
| Acceso en línea: | https://doi.org/10.5281/zenodo.17942951 |
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- <p><span>We introduce Stratified Paraconsistent Logic (SPL), a formal system that handles contradictions through contextual stratification while preserving classical reasoning locally. Unlike existing paraconsistent systems that employ truth-value gluts (LP), consistency operators (LFI), or hierarchical weakening (Cn), SPL implements a graduated spectrum M₀→M₁→M₂ where contradictory propositions coexist in isolated contexts without global logical collapse.</span></p> <p><span>The central innovation is the transgressive object θ—a mathematical primitive whose properties vary across contexts—formalized algebraically as a twist-structure enriched with contextual operators. We establish soundness, completeness, and cut-elimination for SPL's sequent calculus, characterize the algebraic variety of -algebras, and demonstrate practical application to inconsistent database query answering.</span></p> <p><span>SPL provides the first formal framework unifying local classical consistency with global contextual paraconsistency within a single graduated system.</span></p> <p><strong><span>MSC Classification:</span></strong><span> 03B53, 03G27, 68P15</span><br><strong><span>Keywords:</span></strong><span> Paraconsistent logic, contextual semantics, stratified systems, twist-structures, inconsistent databases, transgressive objects.</span></p>