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Building large software systems out of existing software components can save time and cost. These software components range from architectural and design components in different phases of software development. Component technologies lead to increasing productivity and flexibility. However, it also introduces significant problems in ensuring the integrity and reliability of these composed systems because of their complex software topologies, interactions, and transactions. In this paper, we concentrate on the pattern-based design components and their compositions, which are captured as contracts through a composition theory. More specifically, design component contract is defined based on process calculus and logic programming; the properties that related to the design component contract are captured, and tools are used to automatically verify these properties. This research will enhance the capabilities of formal system modeling and analysis by providing a rigorous basis for high-assurance integration of diverse pattern-based components.