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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
본 논문에서는 규칙성과 설정값 함수에 중점을 둡니다. 규칙성은 SC Kleene이 삼항 논리의 명제 연산에서 처음으로 도입했습니다. 그런 다음 M. Mukaidono는 일반 연산으로 표현될 수 있는 삼항 함수의 몇 가지 속성을 조사했습니다. 그는 이러한 삼항 함수를 "정규 삼항 논리 함수"라고 불렀습니다. 일반 삼항 논리 함수는 부울 함수가 처리할 수 없는 이진 논리 회로의 과도 상태 또는 초기 상태와 같은 모호성을 표현하고 분석하는 데 유용합니다. 또한 이진 논리 회로의 안전 장치 시스템 연구에도 적용됩니다. 본 논문에서는 정규 삼항 논리 함수를 다음으로 확장하는 방법에 대해 논의할 것입니다. r비어 있지 않은 하위 집합 집합에 대한 매핑으로 정의되는 값 집합 값 함수 r-값 집합 {0, 1, . . . , r-1}. 먼저, 이 문서에서는 다음 작업을 수행하는 방법을 보여줍니다. r-값 집합 {0, 1, . . . , r-1}은 {0, 1, . . . , r-1}. 이 방법은 Kleene이 이항 논리 연산을 삼항 논리로 확장한 방식과 동일하므로 이러한 연산을 정규 연산이라고 합니다. 마지막으로, 단조로운 집합 값 함수의 명시적 표현은 다음과 같습니다.
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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
부
@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},}
부
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 -