Well Founded Semantics as Two dimensional Here and There

This work presents a new logical characterization of well founded semantics that provides, as interesting innovation, a fully semantic-oriented treatment of program connectives without relying on any syntactic restriction or transformation. Our work is inspired by a recent research line which has established a nice correspondence between stable models and a particular minimization for the monotonic logic of here-and-there. We identify a generalization of the latter (we have called two-dimensional here-and-there) that captures Przymusinki’s 3-valued stable models and show that, as in the 2-valued case, the here-and-there version is more economical in the set of models involved in the minimization process.