Local order degrees (LODs) are evaluation functions, or local objective functions, whose values are defined for a type of atoms or for a pair of types of atoms, using only local information. LODs are functions with one or two arguments:
The arguments are atoms. LODs have a larger value when the local state of the working memory is better, i.e., the state concering to a or a1 and a2 is better. An LOD may be regarded as a negated energy. For example, it is analogous to the bonding energy in chemical reaction systems. Although LODs can be built into normal production rules, the separation of LODs from rules causes a certain flexibility. The separation causes bidirectionality of rules, i.e., LHS and RHS may be interchanged. The separation also makes performance improvement by adding catalysts or rule composition possible.