島根大学総合理工学研究科
ISSN:1342-7121
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Use this link to cite this item : https://ir.lib.shimane-u.ac.jp/3351
Memoirs of the Graduate School of Science and Engineering, Shimane University. Series B, Mathematics 31
1998-03 発行
Characterization Theorem of 4-valued de Morgan Logic
Kondo, Michiro
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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 = {0, a, b, 1};
(2) The Lindenbaum algebra of ML is the MI-algebra;
(3) The completeness theorem of ML is established;
(4) ML is decidable.
(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 = {0, a, b, 1};
(2) The Lindenbaum algebra of ML is the MI-algebra;
(3) The completeness theorem of ML is established;
(4) ML is decidable.
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