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. 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 𝒯-algebras, and demonstrate practical application to inconsistent database query answering. SPL provides the first formal framework unifying local classical consistency with global contextual paraconsistency within a single graduated system. MSC Classification: 03B53, 03G27, 68P15Keywords: Paraconsistent logic, contextual semantics, stratified systems, twist-structures, inconsistent databases, transgressive objects.
J.M Alant (Wed,) studied this question.