クリーネ論理の完全性定理

In this paper we shall define a Kleene logic whose Lindenbaum algebra is the Kleene algebra with implication (simply called i-Kleene algebra) and show that
(1) Every i-Kleene algebra can be embedded to the simplest i-Kleene algebra 3 = {O,1/2,1};
(2) The Lindenbaum algebra of the Kleene logic is an i-Kleene algebra ;
(3) The completeness theorem of the Kleene logic is established ;
(4) The Kleene logic is decidable.