From the research on logics without tautologies (part 1)

The aim of this cycle of papers is to provide characterizations of various logical systems without tautologies (LWT). Kleene's logic is a paradigmatic example of an LWT. The first section contains four equivalent descriptions of this logic due to Simons, Gniazdowski and Boczvar, respectively. Section 2 is concerned with several formalizations of LWTs based on simple two-element logical matrices endowed with one (one- or two-argument) function.