This paper presents a bargaining framework grounded in the methods of conceptual blending and amalgamation to support automated negotiation. The bargaining scenario is represented using a content-rich and descriptive formal language, featuring a subsumption hierarchy among negotiation terms. Bargainers generate proposals or counter-proposals within the amalgam of their initial offers, incorporating unifications of all possible generalizations of these offers. Under this framework, we prove that any bargaining sequence converges to an agreement when each bargainer makes minimal concessions according to their individual preferences. The resulting agreement satisfies individual rationality, collective rationality, Pareto optimality, and contract independence. Furthermore, we show that this solution is uniquely characterized by these properties.