Lvov-Warsaw School. Past and Present (2018)

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic.
Keywords Aristotle’s syllogistic Słupecki’s rejection function   generalization of rejection notion  genesis of rejection notion  rejection in Łukasiewicz’s sense  Słupecki’s solution of decidability problem of Aristotle’s syllogistic  deductive systems  axiomatic method of rejection   refutation systems  Słupecki's rejection function  generalization of rejection notion
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References found in this work BETA

Formalization of Logic.Rudolf Carnap - 1943 - Cambridge: Mass., Harvard University Press.
S. Leśniewski's Calculus of Names.Jerzy Słupecki - 1984 - In Jan T. J. Srzednicki, V. F. Rickey & J. Czelakowski (eds.), Studia Logica. Distributors for the United States and Canada, Kluwer Boston. pp. 59--122.
Dual Counterparts of Consequence Operations.Ryszard Wójcicki - 1973 - Bulletin of the Section of Logic 2 (1):54-57.

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