Characterization Theorem of 4-valued de Morgan Logic
Michiro Kondo · 1998
In this paper we give an axiom system of a non-linear 4-valued logic which we call a de Morgan logic (ML), whose Lindenbaum algebra is the de Morgan algebra with implication (MI-algebra), and show that (1) For every MI-algebra L, there is a quotient MI-algebra L ) such that it is embeddable to the simplest 4-valued MI-algebra M = f0, a, b, 1g; (2) The Lindenbaum algebra of ML is the MI-algebra; (3) The completeness theorem of ML is established; (4) ML is decidable.