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According to Frege's principle the denotation of a sentence coincides with its truth-value. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic… (More)

A deductive system S (in the sense of Tarski) is Fregean if the relation of interderivability, relative to any given theory T , i.e., the binary relation between formulas { α, β : T, α S β and T, β S α }, is a congruence relation on the formula algebra. The multiterm deduction-detachment theorem is a natural generalization of the deduction theorem of the… (More)

A b s t r a c t. A short history of equivalential logics is sketched commencing with the pioneering work of Prucnal and Wro´nski [1974]. The notion of equivalential logic is due to Tadeusz Prucnal and Andrzej Wro´nski. The short note " An algebraic characterization of the notion of structural completeness " appeared in 1974 in Bulletin of the Section of… (More)