Cyclic A-infinity algebras and their Koszul duals

The notion of a cyclic A-infinity algebra appears naturally in many contexts of algebra and topology, e.g. as cochain algebras of Poincare duality spaces. It is important to characterize intrinsically their Koszul duals. Such a characterization was provided in a recent work of Van den Berg but inly under rather restrictive grading assumptions that are, in particular, exclude the example mentioned above. The goal of this project is to remove these assumptions and also refine the characterization to the commutative case. A corollary would be an intrinsic characterization of homotopy Lie algebras of Poincare duality spaces.