Some Properties of Kleene-Stone Logic Functions and Their Canonical Disjunctive Form

Noboru TAKAGI; Masao MUKAIDONO

Some Properties of Kleene-Stone Logic Functions and Their Canonical Disjunctive Form

Noboru TAKAGI, Masao MUKAIDONO

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In this paper, we will define Kleene-Stone logic functions which are functions F: [0, 1]ⁿ[0, 1] including the intuitionistic negation into fuzzy logic functions, and they can easily represent the concepts of necessity and possibility which are important concepts of many-valued logic systems. A set of Kleene-Stone logic functions is one of the models of Kleene-Stone algebra, which is both Kleene algebra and Stone algebra, as same as a set of fuzzy logic functions is one of the models of Kleene algebra. This paper, especially, describes some algebraic properties and representation of Kleene-Stone logic functions.

Publication: IEICE TRANSACTIONS on Information Vol.E76-D No.2 pp.163-170

Publication Date: 1993/02/25

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Type of Manuscript: PAPER

Category: Computer Hardware and Design

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Noboru TAKAGI, Masao MUKAIDONO, "Some Properties of Kleene-Stone Logic Functions and Their Canonical Disjunctive Form" in IEICE TRANSACTIONS on Information, vol. E76-D, no. 2, pp. 163-170, February 1993, doi: .
Abstract: In this paper, we will define Kleene-Stone logic functions which are functions F: [0, 1]ⁿ[0, 1] including the intuitionistic negation into fuzzy logic functions, and they can easily represent the concepts of necessity and possibility which are important concepts of many-valued logic systems. A set of Kleene-Stone logic functions is one of the models of Kleene-Stone algebra, which is both Kleene algebra and Stone algebra, as same as a set of fuzzy logic functions is one of the models of Kleene algebra. This paper, especially, describes some algebraic properties and representation of Kleene-Stone logic functions.
URL: https://global.ieice.org/en_transactions/information/10.1587/e76-d_2_163/_p

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@ARTICLE{e76-d_2_163,
author={Noboru TAKAGI, Masao MUKAIDONO, },
journal={IEICE TRANSACTIONS on Information},
title={Some Properties of Kleene-Stone Logic Functions and Their Canonical Disjunctive Form},
year={1993},
volume={E76-D},
number={2},
pages={163-170},
abstract={In this paper, we will define Kleene-Stone logic functions which are functions F: [0, 1]ⁿ[0, 1] including the intuitionistic negation into fuzzy logic functions, and they can easily represent the concepts of necessity and possibility which are important concepts of many-valued logic systems. A set of Kleene-Stone logic functions is one of the models of Kleene-Stone algebra, which is both Kleene algebra and Stone algebra, as same as a set of fuzzy logic functions is one of the models of Kleene algebra. This paper, especially, describes some algebraic properties and representation of Kleene-Stone logic functions.},
keywords={},
doi={},
ISSN={},
month={February},}

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TY - JOUR
TI - Some Properties of Kleene-Stone Logic Functions and Their Canonical Disjunctive Form
T2 - IEICE TRANSACTIONS on Information
SP - 163
EP - 170
AU - Noboru TAKAGI
AU - Masao MUKAIDONO
PY - 1993
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E76-D
IS - 2
JA - IEICE TRANSACTIONS on Information
Y1 - February 1993
AB - In this paper, we will define Kleene-Stone logic functions which are functions F: [0, 1]ⁿ[0, 1] including the intuitionistic negation into fuzzy logic functions, and they can easily represent the concepts of necessity and possibility which are important concepts of many-valued logic systems. A set of Kleene-Stone logic functions is one of the models of Kleene-Stone algebra, which is both Kleene algebra and Stone algebra, as same as a set of fuzzy logic functions is one of the models of Kleene algebra. This paper, especially, describes some algebraic properties and representation of Kleene-Stone logic functions.
ER -