The Disjunction-Free Fragment of D2 is Three-Valued

TL;DR

This paper proves that the disjunction-free fragment of Jaśkowski's discussive logic D2 is complete with respect to three- and four-valued semantics, providing a simple axiomatization and discussing its implications.

Contribution

It establishes completeness and provides a simple axiomatization for the disjunction-free fragment of D2, a notable result in non-classical logic.

Findings

Completeness of the fragment with respect to three- and four-valued semantics

A simple axiomatization of the disjunction-free fragment of D2

Discussion of implications of the completeness result

Abstract

In this article, the disjunction-free fragment of Ja\'skowski's discussive logic D2 in the language of classical logic is shown to be complete with respect to three- and four-valued semantics. As a byproduct, a rather simple axiomatization of the disjunction-free fragment of D2 is obtained. Some implications of this result are also discussed.