TY - GEN
T1 - Implicational tonoid fuzzy logics
AU - Yang, Eunsuk
N1 - Publisher Copyright:
© 2018 The authors and IOS Press. All rights reserved.
PY - 2018
Y1 - 2018
N2 - This paper deals with one class of propositional fuzzy logics. Recently, fuzzy logic systems have been introduced as logics being complete with respect to linearly ordered algebras, in particular, algebras on the unit interval [0,1]. One of important trends in this logic is to introduce logic systems having more general structures. As one work of this trend, we introduce implicational tonoid fuzzy logics as fuzzy logics with tonic properties. For this, we first define implicational tonoid fuzzy logics in general. We then introduce their corresponding ternary relational semantics, called Routley–Meyer–style semantics. Routley–Meyer semantics was first introduced as semantics for relevance logics and then has been generalized to semantics for other non-classical logics. Finally, we prove that implicational tonoid fuzzy logics are sound and complete with respect to their corresponding Routley–Meyer–style semantics.
AB - This paper deals with one class of propositional fuzzy logics. Recently, fuzzy logic systems have been introduced as logics being complete with respect to linearly ordered algebras, in particular, algebras on the unit interval [0,1]. One of important trends in this logic is to introduce logic systems having more general structures. As one work of this trend, we introduce implicational tonoid fuzzy logics as fuzzy logics with tonic properties. For this, we first define implicational tonoid fuzzy logics in general. We then introduce their corresponding ternary relational semantics, called Routley–Meyer–style semantics. Routley–Meyer semantics was first introduced as semantics for relevance logics and then has been generalized to semantics for other non-classical logics. Finally, we prove that implicational tonoid fuzzy logics are sound and complete with respect to their corresponding Routley–Meyer–style semantics.
KW - Gaggle logic
KW - Implicational tonoid (fuzzy) logic
KW - Relational semantics
KW - Routley–Meyer–style semantics
KW - Weakly implicative (fuzzy) logic
UR - https://www.scopus.com/pages/publications/85057297481
U2 - 10.3233/978-1-61499-927-0-223
DO - 10.3233/978-1-61499-927-0-223
M3 - Conference paper
AN - SCOPUS:85057297481
T3 - Frontiers in Artificial Intelligence and Applications
SP - 223
EP - 230
BT - Fuzzy Systems and Data Mining IV - Proceedings of FSDM 2018
A2 - Tallon-Ballesteros, Antonio J.
A2 - Li, Kaicheng
PB - IOS Press BV
T2 - 4th International Conference on Fuzzy Systems and Data Mining, FSDM 2018
Y2 - 15 November 2018 through 16 November 2018
ER -