Abstract
We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) ⊑ L and p, A(p, q) ⊢s q.
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References
W.J. Blok and D. Pigozzi, Protoalgebraic logics, Studia Logica 45 (1986), pp. 337–369.
W.J. Blok and D. Pigozzi, Algebraizable logics, Memoirs of American Mathematical Society 77 (1989), American Mathematical Society, Providence.
W.J. Blok and D. Pigozzi, The deduction theorem in algebraic logic, (to appear)
W.J. Blok and D. Bigozzi, Algebraic semantics for universal Horn logic without equality, Universal Algebra and Quasigroups, Heldermann Verlag, Berlin, (to appear)
J. Czelakowski, Algebraic aspects of deduction theorems, Studia Logica 44 (1985), pp. 369–387.
J. Czelakowski, Local deduction theorems, Studia Logica 45 (1986), p. 377–391.
J. czelakowski and W. dziobiak, The deduction-like theorem for quasivarieties of algebras and its applications, (preprint)
J. Perzanowski and A. Wroński, The deduction theorem for the system T of Feys-von Wright, Universitas lagiellonica Acta Scientiarum Literarumque, CCLXV, Schediae Logicae, fasc VI (1971), pp. 11–14.
W.A. Pogorzelski, Przeglad twierdzeń o dedukeji dla rachunków zdaniowych, Studia Logica 15 (1964), pp. 163–178.
M. Tokarz, Deduction theorems for RM and its extensions, Studia Logica 38 (1979), pp. 105–111.
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Czelakowski, J., Dziobiak, W. A deduction theorem schema for deductive systems of propositional logics. Stud Logica 50, 385–390 (1991). https://doi.org/10.1007/BF00370679
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DOI: https://doi.org/10.1007/BF00370679