Term declaration logic and generalised composita

A generalization of a version of order-sorted logic and an abstract axiomatic setting for the treatment of substitution are given. The two ideas are shown to be related, an equational specification of term declaration logic being a presentation of a finitary generalized composition. The automatic approach to substitution is compared with some other approaches. The relationship between algebraic theories and standard equational logic is reviewed. One of the aims is to lay the foundations for a generalization of these connections to connections between term declaration logic and finitary generalized composita and a suitable generalization of algebraic theories