Preservation theorems hold for all lattice semirings but fail for tropical, Viterbi, Łukasiewicz, and natural semirings, while existential preservation holds on finite interpretations for lattices unlike the Boolean case.
The Computational Complexity of Provability in Systems of Modal Propositional Logic.SIAM Journal on Computing1977,6(3), 467–480
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Biprofile deviation logic proves soundness and completeness of H_bp for Dev(N) frames and introduces typed manipulation witnesses, boundary-row theorem, and factor-closure criterion for auditing report changes.
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Preservation Theorems in Semiring Semantics
Preservation theorems hold for all lattice semirings but fail for tropical, Viterbi, Łukasiewicz, and natural semirings, while existential preservation holds on finite interpretations for lattices unlike the Boolean case.
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Biprofile Deviation Logic: Report-Replacement Frames and Audit Witnesses
Biprofile deviation logic proves soundness and completeness of H_bp for Dev(N) frames and introduces typed manipulation witnesses, boundary-row theorem, and factor-closure criterion for auditing report changes.