Predicate logics without the structure rules
In our previous paper [\textit{H. Ono} and \textit{Y. Komori}, J. Symb. Logic 50, 169-201 (1985; Zbl 0583.03018)], we have studied Kripke-type semantics for propositional logics without the contraction rule. In this paper, we will extend our argument to predicate logics without the structure rules. Similarly to the propositional case, we cannot carry out Henkin's construction in the predicate case. Besides, there exists a difficulty that the rules of inference (\(\to \forall)\) and (\(\exists \to)\) are not always valid in our semantics. So, we have to introduce a notion of normal models.
predicate logics without the structure rules
scientific article; zbMATH DE number 4004149