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Companies nowadays are under increasing pressure to adapt their business processes to the ever-changing business environment. However, most traditional business process modeling (BPM) methods lack enough flexibility. It is hard to extract and reuse information and knowledge embedded in the existing business process models to build new models. We propose an algebraic framework based on a many-sorted algebra, algebra of system (AoS), to achieve the flexibility in business process modeling. We decompose business process models into different modules of knowledge and encode them as different algebraic domains of AoS. Within each algebraic domain, knowledge is encoded as operands. Based on operands, each algebraic domain is equipped with operators to provide computation capabilities. The operands and operators ensure the flexibility that the framework can achieve and the analysis capabilities that the framework can provide.