Modal logics with n ‐ary connectives

The aim of this paper is to provide a general framework in order to present from a unitary point of view considerable experience in the field of non classical logics. Usual modal logic deals with a binary relation and a unary operator (generalizations to many binary relations and many unary operators are straightforward at least in the initial stage); although n-ary operators and n + 1-ary relations have been only partially investigated (see [9] where there is also a representation theorem) the experience of the semantics of relevant logics [25] shows how to manage the case of ternary relations.