Towards Łukasiewicz

Abstract

The paper contains an attempt at formulating the project of logic comprised in Jan Łukasiewicz's article „On determinism” and a construction of a logic which would realise this project. Such a logic consists of three consequence-operations build upon a four-element algebra. The values of the algebra have been defined by means of the following set of sentences: true and true today, true but not true today, false but not false today and false and false today. It turns out that only one of the consequences is different from the classical consequence and all of them are logically two-valued. It is proved moreover, that the assumption that tautologies consists of sentences-forms which are „always” true today, results in the non-existence of such tautologies.