In the late forties, Stanisław Jaśkowski published two papers onthe discursive sentential calculus, D2. He provided a definition of it by an interpretation in the language of S5 of Lewis. The knownaxiomatization of D2 with discursive connectives as primitives was introduced by da Costa, Dubikajtis and Kotas in 1977. It turns out, however,that one of the axioms they used is not a thesis of the real Jaśkowski’s calculus. In fact, they built a new system, D∗2 for short, that differs from (...) D2 inmany respects. The aim of this paper is to introduce a direct Kripke-type semantics for the system, axiomatize it in a new way and prove soundness andcompleteness theorems. Additionally, we present labelled tableaux for D∗2.1. (shrink)

In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB1, is an extension of systems PI, C min and B1, and a proper subsystem of Sette’s calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi.

Discursive (or discussive) logic, D₂, introduced by Jaśkowski, is widely recognized as a first formal approach to paraconsistency. Jaśkowski applied a quite extraordinary technique at that time to describe his logic. He neither gave a set of the axiom schemata nor presented a direct semantics for D₂ but used a translation function to express his philosophical and logical intuitions. Discursive logic was defined by an interpretation in the language of S₅ of Lewis. The aim of this paper is to present (...) a modified system of the discursive logic that allows some of the weaker versions of Duns Scotus's thesis to be valid. The initial idea is to consider a different characteristic of the connective of negation. We introduce both a direct semantics and an axiomatization of the new system, prove the key metatheorems, and describe labeled tableaux for the system. (shrink)

In 1948, Stanis aw Ja kowski defined a logical system D2 of a discursive 1 sentential calculus. The aim of this paper is to introduce the reader to the basic ideas of the discursive logic and to show, in a historical perspective, its development originating from the two germ papers [19] and [20]. We intend to present some problems connected with it and outline the solutions they have received up to the present day.

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.