A variety of business relationships in open settings can be understood in terms of the creation and manipulation of commitments among the participants. These include B2C and B2B contracts and processes, as realized via Web services and other such technologies. Business protocols, an interaction-oriented approach for modeling business processes, are formulated in terms of the commitments. Commitments can support other forms of semantic service composition as well. This paper shows how to represent and reason about commitments in a general manner. Unlike previous formalizations, the proposed formalization accommodates complex and nested commitment conditions, and concurrent commitment operations. In this manner, a rich variety of open business scenarios are enabled.