Janusz Czelakowski

Learn More
According to Frege’s principle the denotation of a sentence coincides with its truthvalue. 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)
The notion of local deduction theorem (which generMizes on the known, instances of indeterminate deduction theorems, e.g. for the infinitely-vMued Lukasiewicz logic Coo) is defined. It is then shown that a given finitary non-pathological logie C admits the local deduction theorem iff the class Mat~(C) of M1 matrices validating 0 ~ has the C-filter extension(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(More)
The aim el the article is to outline the historical background and the present state of the methodology of deductive systems invented by Alfred Tarski in the thirties. Key notions of Tax'ski's methodology are presented and discussed through the recent development of the original concepts ~nd ideas. w 1. Consequence operations Philosophical intuit ions which(More)
deductive system S of a propositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only propositional letters p and q such that A(p, p) C_ L and p, A(p, q) ~-s q. Since the discovery of the deduct ion theorem by Tarski and Herbrand much a t ten t ion has been paid to searching for(More)
The notion of equivalential logic is due to Tadeusz Prucnal and Andrzej Wroński. The short note “An algebraic characterization of the notion of structural completeness” appeared in 1974 in Bulletin of the Section of Logic, Vol. 3, 30-33. The work dealt mainly with structural completeness, the property of deductive systems which was systematically(More)