Abstract
There are syntactically identifiable situations in which reduction does not occur in chain format linear deduction systems, i.e. situations in which linear-input subdeductions are performed. Three methods of detecting these situations are described in this paper. The first method (Horn subset analysis) focuses on Horn input chains while the second (LISS analysis) and third (LISL analysis) are successive generalisations of the first method. A significant benefit that may be derived from detecting linear-input subdeductions is the applicability of a truth value deletion strategy in such subdeductions. The completeness of the deletion strategy is proved, and its efficacy indicated.