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Essential variables and positions in terms (0802.2385v4)
Published 17 Feb 2008 in math.GM, cs.IT, and math.IT
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 $\Sigma$.