A Frame-based Characterisation of the Paraconsistent Well-founded Semantics with Explicit Negation

In this work, we present Paraconsistent Well-Founded Semantics with eXplicit negation (WFSXp) by introducing a frame-based semantics. As far as we know, this is the first time that a declarative approach for WFSXp is effectively characterised in terms of a model theory. Dismissing usual techniques based on immediate consequence operators, our definition depicts WFSXp by minimising models satisfying particular criteria. Aware that WFSXp captures a large deal of logic programming semantics (including the main well-founded ones), our approach subsumes indirectly a semantics for them. Then assuming an illustrative tone, by adding some conditions, we also show how it can be adjusted to define Well-Founded Semantics with eXplicit negation (WFSX ), WellFounded Semantics (WFS) as well as Answer Sets. Given its declarative aspects, our work paves the way to define a logical representation of the family of well-founded semantics.