Faculty of Science, Shimane University
ISSN:0387-9925
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Use this link to cite this item : https://ir.lib.shimane-u.ac.jp/686
Memoirs of the Faculty of Science, Shimane University 29
1995-12-25 発行
クリーネ論理の完全性定理
Completeness Theorem of Kleene Logic
Kondo, Michiro
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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.
(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.
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