Algebraic Kripke-Style Semantics for Relevance Logics

Substructural Inquisitive Logics

“…A suitable semantic framework that we are going to introduce and use is strongly inspired by (Došen, 1989). The framework also has many similarities with various other semantics that have appeared in the literature on nonclassical logics, for example in (Urquhart, 1972;Fine, 1974;Wansing, 1993;Fine, 2014;Yang, 2014).…”

Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

“…Although these two valuations are not free from the above negative fact, they have been extensively used in substructural logics: Using (→ • U ), many logicians such as Došen and Ono have introduced similar semantics for modal and substructural logics [14][15][16]; with the title "Kripke-style semantics", Montagna-Ono [17], Montagna-Sacchetti [18], and Yang [19,20] introduced similar semantics for substructural fuzzy logics. Using (→ • F ), logicians such as Ono-Komori [21], Ishihara [22], and Kamide [23] have introduced analogous semantics for some (modal) substructural logics (For more detailed introduction of these semantics, see [1]).…”

“…The more detailed other reasons to study this are as follows: The first and most important reason is that while algebraic Kripke-style (briefly AK) semantics (The term AK semantics means semantics with operations in place of binary accessibility relations, the frames of which have the same structures as algebraic semantics.) for substructural fuzzy logics have been introduced extensively (see, e.g., [17][18][19][20][30][31][32]), ARM semantics for such logics have not. Only, the author [33,34] introduced such semantics for MTL (Monoidal t-norm logic) and its involutive extension IMTL.…”