Łukasiewicz, Jan (1878–1956)

Before 1918, Łukasiewicz’s interests centred on logic (in the broad sense) and philosophy, and he worked on induction and probability. He also wrote an important historical book on the principle of contradiction in Aristotle. After 1918, Łukasiewicz concentrated almost entirely on mathematical logic and was the main organizer of the Warsaw School of Logic. The discovery of many-valued systems of logic is perhaps the most important result he achieved. He also invented an ingenious logical symbolism in which brackets (or other punctuation signs) are not necessary (bracket-free or Polish notation). Propositional calculi became a favourite topic of Łukasiewicz’s logical investigations. The history of logic was another subject in which Łukasiewicz achieved important results.

Potoses: Categorical Paraconsistent Universum for Paraconsistent Logic and Mathematics

It is well-known that the concept of da Costa algebra [3] reects most of the logical properties of paraconsistent propositional calculi $C_{n},1\leq n\leq \omega $ introduced by $N.C.A.$ da Costa. In [10] the construction of topos of functors from a small category to the category of sets was proposed which allows to yield the categorical semantics for da Costa's paraconsistent logic. Another categorical semantics for $C_{n}$ would be obtained by introducing the concept of $\textit{potos}$ { the categorical counterpart of da Costa algebra (the name "potos" is borrowed from W.Carnielli's story of the idea of such kind of categories) DOI: 10.21146/2074-1472-2017-23-2-76-95

A note on entropy of logic

We propose an entropy based classification of propositional calculi. Our method can be applied to finite?valued propositional logics and then, extended asymptotically to infinite?valued logics. In this paper we consider a classification depending on the number of truth values of a logic and not on the number of its designated values. Furthermore, we believe that almost the same approach can be useful in classification of finite algebras.