A Syntactic Stratification Condition Using Constraints

Stratification conditions for logic programs aim to ensure a two-valued semantics by restricting the class of allowable programs. Previous stratification conditions suffer from one of two problems. Some (such as modular stratification and weak stratification) are semantic, and cannot be recognized without examining the facts in addition to the rules of the program. Others (such as stratification and local stratification) are syntactic, but do not allow a number of useful examples. A nonsemantic version of modular stratification, i.e., whether a program is modularly stratified for all extensional databases, is shown to be undecidable. We propose a condition that generalizes local stratification, that ensures a two-valued well-founded model, and that can be syntactically determined from the rules and some constraints on the facts in the program. We call this condition "Universal Constraint Stratification." While not every modularly stratified program is universally constraint stratified,..