The Well-founded semantics is not the only semantics for non-stratified programs. XSB can be used to (help) implement other semantics that lie in one of two classes. 1) Semantics that extend the well-founded semantics to include new program constructs; or 2) semantics that contain the well-founded partial model as a submodel.
An example of a semantics of class 1) is (WFSX) [3], which adds explicit (or provable) negation to the default negation used by the Well-founded semantics. The addition of explicit negation in WFSX, can be useful for modeling problems in domains such as diagnosis and hierarchical reasoning, or domains that require updates [32], as logic programs. WFSX is embeddable into the well-founded semantics; and this embedding gives rise to an XSB meta-interpreter, or, more efficiently, to the preprocessor described in Section Extended Logic Programs in Volume 2. See [47] for an overview of the process of implementing extensions of the well-founded semantics.
An example of a semantics of class 2) is the stable model semantics. Every stable model of a program contains the well-founded partial model as a submodel. As a result, the XSB can be used to evaluate stable model semantics through the residual program, to which we now turn.