Symmetric Structure in Logic Programming

Abstract
It is argued that some symmetric structure in logic programs could be taken into account when implementing semantics in logic programming. This may enhance the declarative ability or expressive power of the semantics. The work presented here may be seen as representative examples along this line. The focus is on the derivation of negative information and some other classic semantic issues. We first define a permutation group associated with a given logic program. Since usually the canonical models used to reflect the common sense or intended meaning are minimal or completed models of the program, we expose the relationships between minimal models and completed models of the original program and its socalled Greduced form newlyderived via the permutation group defined. By means of this Greduced form, we introduce a rule to assume negative information termed GCWA, which is actually a generalization of the GCWA. We also develop the notions of Gdefinite, Ghierarchical and Gstratified logic programs, which are more general than definite, hierarchical and stratified programs, and extend some wellknown declarative and procedural semantics to them, respectively.

