Implicational Tonoid Logics and Implicational Partial Galois Logics

Abstract

Implicational Tonoid Logics: Algebraic and Relational Semantics This paper combines two classes of generalized logics, one ofwhich is the class of weakly implicative logics introduced by Cintula andthe other of which is the class of gaggle logics introduced by Dunn. Forthis purpose we introduce implicational tonoid logics. More precisely, wefirst define implicational tonoid logics in general and examine their rela-tion to weakly implicative logics. We then provide algebraic semanticsfor implicational tonoid logics. Finally, we consider relational semantics,called Routley–Meyer–style semantics, for finitary those logics. Implicational Partial Galois Logics: Relational Semantics Implicational tonoid logics and their relational semantics havebeen introduced by Yang and Dunn. This paper extends this investigationto implicational partial Galois logics. For this, we first define some impli-cational partial gaggle logics as special kinds of implicational tonoid logicscalled “implicational partial Galois logics.” Next, we provide Routley–Meyer-style relational semantics for finitary those logics.