"Bilattices and frames are mathematical structures widely applied in Theoretical Computer Science, although in quite different areas.Bilattices were introduced within the context of non-monotonic and paraconsistent reasoning in Artificial Intelligence, while frames have a key role in Domain Theory, the mathematical theory of computation introduced by Dana Scott as a foundation for denotational semantics of programs.The introduction of d-frames, a generalization of frames designed to handle partial and conflicting information, has recently opened a way to combine these two formalisms.The aim of the present proposal is to explore this possibility in order to obtain a mathematically rigorous and versatile formalism that unifies the approach of bilattices and the one of d-frames, thus having a primary impact on Domain Theory but also on bilattice-based formalisms.This is to be accomplished, on the one hand, by applying the algebraic and logical methods that proved to be successful in the study of bilattices to the theory of d-frames, with the main aim to develop and achieve a deeper understanding of the logic underlying d-frames; on the other hand, by extending the scope of bilattices to the setting of Domain Theory, focusing on issues such as completeness and topological duality.This is to be accomplished by (1) applying the algebraic and logical methods that proved to be successful in the study of bilattices to the theory of d-frames, with the main aim of developing and achieving a deeper understanding of the logic underlying d-frames; and by (2) extending the scope of bilattices to the setting of Domain Theory, focusing on issues such as completeness and topological duality."