Data Exchange is an old problem that was firstly studied from a theoretical point of view only in 2003. Since then many approaches were considered when it came to the language describing the relationship between the source and the target schema. These approaches focus on what it makes a target instance a "good" solution for data-exchange. In this paper we propose the inference-based semantics that solves many certain-answer anomalies existing in current data-exchange semantics. To this we introduce a new mapping language between the source and the target schema based on annotated bidirectional dependencies (abd) and, consequently define the semantics for this new language. It is shown that the ABD-semantics can properly represent the inference-based semantics, for any source-to-target mappings. We discovered three dichotomy results under the new semantics for solution-existence, solution-check and UCQ evaluation problems. These results rely on two factors describing the annotation used in the mappings (density and cardinality). Finally we also investigate the certain-answers evaluation problem under ABD-semantics and discover many tractable classes for non-UCQ queries even for a subclass of CQ with negation.