Stratified Paraconsistent Logic (SPL)
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| Natura: | Recurso digital |
| Lingua: | inglese |
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Zenodo
2025
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| _version_ | 1866901339378810880 |
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| author | Alant, J.M. |
| author_facet | Alant, J.M. |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17942951 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Stratified Paraconsistent Logic (SPL) Alant, J.M. Paraconsistent logic contextual semantics stratified systems twist-structures inconsistent databases transgressive objects MSC: 03B53 MSC: 03G27 MSC: 68P15 <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> |
| title | Stratified Paraconsistent Logic (SPL) |
| topic | Paraconsistent logic contextual semantics stratified systems twist-structures inconsistent databases transgressive objects MSC: 03B53 MSC: 03G27 MSC: 68P15 |
| url | https://doi.org/10.5281/zenodo.17942951 |