Some Properties and a Necessary and Sufficient Condition for Extended Kleene-Stone Logic Functions (Special Issue on Multiple-Valued Logic)
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概要
- 論文の詳細を見る
Recently, fuzzy logic which is a kind of infinite multiple-valued logic has been studied to treat certain ambiguities, and its algebraic properties have been studied by the name of fuzzy logic functions. In order to treat modality (necessity, possibility) in fuzzy logic, which is an important concept of multiple-valued logic, the intuitionistic logical negation is required in addition to operations of fuzzy logic. Infinite multiple-valued logic functions introducing the intuitionistic logical negation into fuzzy logic functions are called Kleene-Stone logic functions, and they enable us to treat modality. The domain of modality in which Kleene-Stone logic functions can handle, however, is too limited. We will define α-KS logic functions as infinite multiple-valued logic functions using a unary operation instead of the intuitionistic logical negation of Kleene-Stone logic functions. In α-KS logic functions, modality is closer to our feelings. In this paper we will show some algebraic properties of α-KS logic functions. In particular we prove that any n-variable α-KS logic function is determined uniquely by all inputs of 7 values which are 7 specific truth values of the original infinite truth values. This means that there is a bijection between the set of α-KS logic functions and the set of 7-valued α-KS logic functions which are restriction of α-KS logic functions to 7 specific truth values. Finally, we show a necessary and sufficient condition for a 7-valued logic function to be a 7-valued α-KS logic function.
- 社団法人電子情報通信学会の論文
- 1993-05-25
著者
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Mukaidono Masao
Department of Computer Science, Meiji University
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Mukaidono Masao
Meiji University
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Mukaidono Masao
School Of Science And Technology Meiji University
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Mukaidono M
Meiji Univ. Kawasaki‐shi Jpn
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Takagi N
Toyama Prefectural Univ. Toyama‐shi Jpn
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Takagi Noboru
Faculty Of Engineering Toyama Prefectural University
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Nakashima Kyoichi
Faculty of Engineering, Toyama Prefectural University
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Nakashima K
Toyama Prefectural Univ. Toyama‐shi Jpn
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Nakashima Kyoichi
Faculty Of Engineering Toyama Prefectural University
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