A non-monotonic ATMS based on annotated logic programs with strong negation

Abstract

In this paper, we translate Dressler's nonmonotonic ATMS with out-assumptions [Dr88] into an annotated logic program with strong negation (ALPSN) which was proposed in [NS94]. Nonmonotonic justifications and assumption nodes of Dressler's ATMS are translated into annotated logic program clauses with strong negation. The most important semantics for Dressler's ATMS is the extension. On the other hand, the corresponding ALPSN has the stable model semantics. We show that there is a one-to-one correspondence between the nonmonotonic ATMS extensions and the corresponding ALPSN stable models with respect to the translation. Dressler's ATMS includes two meta-rules of inference, the Consistent Belief Rule and the Nogood Inference Rule, and an axiom, the Negation Axiom. We also show that these inference rules and the axiom can be reduced into the ALPSN stable model computation. We take an example of the nonmonotonic ATMS based on ALPSNs (the ALPSN stable model computing system) and show how the ATMS works. Lastly, we indicate the advantages and the problems to be solved of the nonmonotonic ATMS based on ALPSNs, and mention future work.