Paraconsistent logic in Poland: A look beyond the discursive logic
University of Łodz, Poland
Stanisław Jaśkowski was a Polish mathematician, logician and philosopher. He is considered to be one of the first to propose a formal calculus of paraconsistent logic. The calculus is widely known under the name ‘Discursive (or Discussive) Logic’ and the abbreviation D2. Discursive Logic shows the importance of a philosophical explanation for a formal approach to natural language. Usually in a discussion, people exchange ideas, share information, express emotions, etc. They may use some vague or imprecise predicates either purposefully or unintentionally. In thinking about sentences like ‘He is smart’, ‘He is bald’ or ‘He is famous’, one might be confused as to how to assign truth or falsity. This can lead to a seeming contradiction. In contrast to D2, the classical and many non-classical logics are not too helpful to gain an insight into the nature of such contradictions.
Discursive Logic is defined through an interpretation of the language of S5 of Lewis. Jaśkowski did not propose any axiomatization nor a direct semantics for his calculus. This gave an impetus for further research on the subject. Huge number of publications appeared, as a result.
In my talk, I am going to show, in a historical perspective, the development of Discursive Logic originating from the two famous Jaśkowski’s papers, that is, “A Propositional Calculus for Inconsistent Deductive Systems” and “On the Discussive Conjuntion in the Propositional Calculus for Inconsistent Deductive Systems”. I will also look beyond D2 and consider new trends in paraconsistent logic in Poland.