The Well Supported Semantics for Multidimensional Dynamic Logic Programs

Multidimensional dynamic logic programs are a paradigm which allows to express (partially) hierarchically ordered evolving knowledge bases through (partially) ordered multi sets of logic programs. They solve contradictions among rules in different programs by allowing rules in more important programs to reject rules in less important ones. This class of programs extends the class of dynamic logic program that provides meaning to sequences of logic programs. Recently the refined stable model semantics has fixed some counterintuitive behaviour of previously existing semantics for dynamic logic programs. However, it is not possible to directly extend the definitions and concepts of the refined semantics to the multidimensional case and hence more sophisticated principles and techniques are in order. In this paper we face the problem of defining a proper semantics for multidimensional dynamic logic programs by extending the idea of well supported model to this class of programs and by showing that this concept alone is enough for univocally characterizing a proper semantics. We then show how the newly defined semantics coincides with the refined one when applied to sequences of programs.