Concepts incompatibilities arise when business systems adopt different application domain ontologies during their interactions. One approach for resolving such incompatibilities is using an intermediate ontology mapping approach that transforms the exchanged concepts into concepts understandable by the interacting systems. Unfortunately, existing approaches for ontology mapping are known of having limited accuracy. This is because such approaches are basically based on generic schematic relations (such as Is-a and Part-of) and ignore the involved usage context as well as the logic of the involved operation. To overcome this limitation, this paper proposes a novel approach for ontology mapping that uses the conditional substitution semantics of application domain concepts to resolve any arising concepts incompatibilities in a context-sensitive manner. Such conditional substitution semantics are defined with respect to every application domain operation using the proposed Concepts Substitutability Enhanced Graph (CSEG). Experimental results show that the proposed conditional ontology mapping approach provided more accurate mapping results when compared with existing generic ontology mapping approaches.