A Parallel Linear & UR - Derivation System 1 Extended

The exponential size of the search space of the resolution procedure necessitates the use of refined derivation systems, which restrict the search space. Given some fundamental refinements, further refined derivation systems can be developed by combining several fundamental refinements in a single derivation system. The manner in which combinations can be formed is necessarily restricted by the requirement of completeness. An alternative to combining refinements in a single derivation system is to use multiple (refined) derivation systems concurrently. All the component derivation systems of a concurrent derivation system use a common input set, and thus all components can use clauses created by other components. Although hard to quantify, it is this 'cross-fertilisation' between different derivation systems which furnishes the power of concurrent derivation systems. A notable feature of the concurrent approach it is only necessary for one of the component derivation systems to be complete.