A quasi-relevant, connexive 4-valued implicative expansion of Belnap-Dunn logic defining material connexive logic MC

Abstract

In this paper, it is defined a connexive 4-valued implicative expansion of Belnap-Dunn logic we have dubbed LMI4C. It is a quasi relevant logic in the sense that it enjoys the "quasi relevance property". Also, LMI4C defines "material connexive logic" MC. The fact that LMI4C defines classical positive logic C+ is used to provide it with a Hilbert-style formulation presenting LMI4C as an expansion of C+. Said formulation is obtained by using a Belnap-Dunn "two-valued semantics".