Well-Founded Inference and 3-Valued Logics

We deene a simple logical semantics based on minimal models in Lukasiewicz's 3-valued logic, L 3. On normal logic programs it is equivalent to the well-founded semantics (WFS), and on disjunctive programs it is equivalent to the P-stable semantics of Eiter, Leone and Saccc a, hence to Przymusinski's 3-valued stable semantics. One advantage is that it is char-acterised by simple conditions on models in a well-known nonclassical logic and therefore provides insight into the nature of partial stable models from a logical standpoint. It also suggests why the P-stable models are a natural generalisation of WFS to the disjunctive case. In addition, the semantics is not restricted to the syntax of logic programs, but is deened for any ground theories.