Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz [1]. The author, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two types of them in each of the two, depending on the manner of combining their premises with the conclusion through the relation of classical logical entailment. Consequently, the four types of reasoning: 1.1. unilateral deductive (incl. its sub-types: deductive inference and proof), 1.2. bilateral deductive (incl. complete induction), and 2.1. reductive (incl. the sub-types: explanation and verification), 2.2. logically nonvaluable (incl. inference by analogy, statistic inference), correspond to four operators of derivability. They are defined formally on the ground of Tarski's axiomatic theory of deductive systems, by means of the consequence operation Cn [4]. Also, certain metalogical properties of these operators are given, as well as their relations with Tarski's consequence operations Cn+ (Cn+ = Cn) and dual consequences Cn−1 [2,3], and Cn− [5].

References [1] Ajdukiewicz, K.: Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). [2] Słupecki J.: Funkcja Łukasiewicza [Łukasiewicz's Function]. Zeszyty Naukowe Uniwersytetu Wrocławskiego, Seria B, Nr 3, 33-40 (1959). [3] SŁupecki, J., Bryll, G., Wybraniec-Skardowska, U.: Theory of Rejected Propositions, Part I. Stud. Log. 29, 76-123 (1971). [4] Tarski, A.: Über einige fundamentale Begrife der Metamathematik. Comptes Rendus des séances de la Société des Sciences et des Letters de Varsovie 23, 22-29 (1930). [5] Wójcicki, R.: Dual Counterparts of Consequences Operations. Bull. Sect. Log. 2(2), 54-57 (1973)