# CLONE OF LINEAR TERMS AND CLONE OF LINEAR FORMULAS

### Abstract

Terms and formulas are expressed in a ﬁrst-order language which are used to describe properties of algebraic systems consisting a non-empty set together with a sequence of operations and a sequence of relations on this set. In this paper we study on linear terms of type (n) for a natural number n>1, this leads to deﬁne the deﬁnition of linear formulas of type ((n),(m)) for natural numbers n,m > 1. To construct clone of linear terms and clone of linear formulas we give a new concept of the partial superposition operation of linear terms and the partial superposition operation of linear formulas, respectively. Moreover, we show that both of them are satisﬁed the superassociative law and the extension of a many-sorted mapping, which maps a generating system to clone, is an endomorphism.