Towards a Theory of Declarative Knowledge

Abstract We identify a useful class of logic programs with negation, called stratified programs, that disallow certain combinations of recursion and negation. Programs in this class have a simple declarative and procedural meaning based, respectively, on model theory and a back-chaining interpreter. The standard model of a stratified program, which gives the program a declarative meaning and is independent of the stratification, is characterized in two ways. One is based on a fixed point theory of nonmonotonic operators and the other on an abstract declarative characterization. The back-chaining interpreter also determines the standard model. Finally, we prove the consistency of Clark's completion for stratified programs and attempt to clarify the sources of some previously reported difficulties with negation in logic programming.

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