Back and Forth Semantics for Normal, Disjunctive and Extended Logic programs

We deene a logical semantics called back-and-forth, applicable to normal and disjunctive datalog programs as well as to programs possessing a second, explicit or`strong' negation operator. We show that on normal programs it is equivalent to the well-founded semantics (WFS), and that 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. The main advantage is that it is characterised by simple conditions on models in a well-known nonclassical logic and therefore provides a better 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. On extended programs with strong negation, the back-and-forth semantics is apparently new, diiering from answer sets, from WSFX and from the static semantics .