Local deductions theorems

Studia Logica 45 (4):377 - 391 (1986)
The notion of local deduction theorem (which generalizes on the known instances of indeterminate deduction theorems, e.g. for the infinitely-valued ukasiewicz logic C ) is defined. It is then shown that a given finitary non-pathological logic C admits the local deduction theorem iff the class Matr(C) of all matrices validating C has the C-filter extension property (Theorem II.1).
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DOI 10.1007/BF00370271
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J. Czelakowski & D. Pigozzi (2004). Fregean Logics. Annals of Pure and Applied Logic 127 (1-3):17-76.
James G. Raftery (2013). Inconsistency Lemmas in Algebraic Logic. Mathematical Logic Quarterly 59 (6):393-406.

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