The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dalam makalah ini, kami menumpukan pada keteraturan dan fungsi nilai set. Keteraturan pertama kali diperkenalkan oleh SC Kleene dalam operasi proposisi logik ternarynya. Kemudian, M. Mukaidono menyiasat beberapa sifat fungsi ternary, yang boleh diwakili oleh operasi biasa. Dia memanggil fungsi ternary tersebut sebagai "fungsi logik ternary biasa". Fungsi logik ternari biasa berguna untuk mewakili dan menganalisis kesamaran seperti keadaan sementara atau keadaan awal dalam litar logik binari yang tidak dapat diatasi oleh fungsi Boolean. Tambahan pula, ia juga digunakan untuk kajian sistem selamat-gagal untuk litar logik binari. Dalam makalah ini, kita akan membincangkan lanjutan fungsi logik ternary biasa ke dalam r-fungsi bernilai set bernilai, yang ditakrifkan sebagai pemetaan pada set subset yang tidak kosong bagi r-set bernilai {0, 1, . . . , r-1}. Pertama, kertas itu akan menunjukkan kaedah yang mana operasi pada r-set bernilai {0, 1, . . . , r-1} boleh dikembangkan menjadi operasi pada set subset tidak kosong {0, 1, . . . , r-1}. Operasi ini akan dipanggil biasa kerana kaedah ini adalah sama dengan cara Kleene mengembangkan operasi logik binari ke dalam logik ternarinya. Akhir sekali, ungkapan eksplisit bagi fungsi bernilai set monotonik dalam
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Salinan
Noboru TAKAGI, Kyoichi NAKASHIMA, "A Logical Model for Representing Ambiguous States in Multiple-Valued Logic Systems" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 10, pp. 1344-1351, October 1999, doi: .
Abstract: In this paper, we focus on regularity and set-valued functions. Regularity was first introduced by S. C. Kleene in the propositional operations of his ternary logic. Then, M. Mukaidono investigated some properties of ternary functions, which can be represented by regular operations. He called such ternary functions "regular ternary logic functions". Regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states or initial states in binary logic circuits that Boolean functions cannot cope with. Furthermore, they are also applied to studies of fail-safe systems for binary logic circuits. In this paper, we will discuss an extension of regular ternary logic functions into r-valued set-valued functions, which are defined as mappings on a set of nonempty subsets of the r-valued set {0, 1, . . . , r-1}. First, the paper will show a method by which operations on the r-valued set {0, 1, . . . , r-1} can be expanded into operations on the set of nonempty subsets of {0, 1, . . . , r-1}. These operations will be called regular since this method is identical with the way that Kleene expanded operations of binary logic into his ternary logic. Finally, explicit expressions of set-valued functions monotonic in
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_10_1344/_p
Salinan
@ARTICLE{e82-d_10_1344,
author={Noboru TAKAGI, Kyoichi NAKASHIMA, },
journal={IEICE TRANSACTIONS on Information},
title={A Logical Model for Representing Ambiguous States in Multiple-Valued Logic Systems},
year={1999},
volume={E82-D},
number={10},
pages={1344-1351},
abstract={In this paper, we focus on regularity and set-valued functions. Regularity was first introduced by S. C. Kleene in the propositional operations of his ternary logic. Then, M. Mukaidono investigated some properties of ternary functions, which can be represented by regular operations. He called such ternary functions "regular ternary logic functions". Regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states or initial states in binary logic circuits that Boolean functions cannot cope with. Furthermore, they are also applied to studies of fail-safe systems for binary logic circuits. In this paper, we will discuss an extension of regular ternary logic functions into r-valued set-valued functions, which are defined as mappings on a set of nonempty subsets of the r-valued set {0, 1, . . . , r-1}. First, the paper will show a method by which operations on the r-valued set {0, 1, . . . , r-1} can be expanded into operations on the set of nonempty subsets of {0, 1, . . . , r-1}. These operations will be called regular since this method is identical with the way that Kleene expanded operations of binary logic into his ternary logic. Finally, explicit expressions of set-valued functions monotonic in
keywords={},
doi={},
ISSN={},
month={October},}
Salinan
TY - JOUR
TI - A Logical Model for Representing Ambiguous States in Multiple-Valued Logic Systems
T2 - IEICE TRANSACTIONS on Information
SP - 1344
EP - 1351
AU - Noboru TAKAGI
AU - Kyoichi NAKASHIMA
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 1999
AB - In this paper, we focus on regularity and set-valued functions. Regularity was first introduced by S. C. Kleene in the propositional operations of his ternary logic. Then, M. Mukaidono investigated some properties of ternary functions, which can be represented by regular operations. He called such ternary functions "regular ternary logic functions". Regular ternary logic functions are useful for representing and analyzing ambiguities such as transient states or initial states in binary logic circuits that Boolean functions cannot cope with. Furthermore, they are also applied to studies of fail-safe systems for binary logic circuits. In this paper, we will discuss an extension of regular ternary logic functions into r-valued set-valued functions, which are defined as mappings on a set of nonempty subsets of the r-valued set {0, 1, . . . , r-1}. First, the paper will show a method by which operations on the r-valued set {0, 1, . . . , r-1} can be expanded into operations on the set of nonempty subsets of {0, 1, . . . , r-1}. These operations will be called regular since this method is identical with the way that Kleene expanded operations of binary logic into his ternary logic. Finally, explicit expressions of set-valued functions monotonic in
ER -