With the development of the IT industry, agility and dynamicity are the two expected characteristics from any business enterprise. Service oriented architecture (SOA) is emerging as a promising approach aiming to address the current trends/needs of enterprise business applications. The current work aims at giving an overview of the conceptual model of SOA based on set theory approach. Also, it posits mathematical definitions for service, logical service, environment service and application definition with the help of general systems theory and mathematical foundation. With the help of mathematical model, the definition and functionality of services enhances SOA principles which can be used efficiently in integrating heterogeneous components.