Essential variables and positions in terms

Abstract

The paper deals with $\Sigma -$composition of terms, which allows us to extend the derivation rules in formal deduction of identities. The concept of essential variables and essential positions of terms with respect to a set of identities is a key step in the simplification of the process of formal deduction. $\Sigma -$composition of terms is defined as replacement between $\Sigma$-equal terms. This composition induces $\Sigma R-$deductively closed sets of identities. In analogy to balanced identities we introduce and investigate $\Sigma -$balanced identities for a given set of identities $\Sigma$.

17 pages, 2 figures

References in corpus (2)

• Essential Variables and Separable Sets in Universal Algebra
• Multi-Hypersubstitutions and Colored Solid Varieties