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Social approaches have been put forward to define semantics for intelligent agent communication messages and to tackle the shortcomings of mental approaches. Formal semantics of those social approaches can be model checked as they are focused on public behaviors instead of private mental states. Social conditional commitments are essential concepts in social approaches that can effectively model agent communications. However, conditional commitments exclusively are not able to model agent communication actions, the cornerstone of the fundamental agent communication theory, namely speech act theory. These actions provide mechanisms for dynamic interactions and enable designers to track the evolution of active conditional commitments. From the perspective of model checking, we need to define a formal and computationally grounded semantics for relevant social actions that can directly be applied to active conditional commitments. This manuscript describes a new symbolic model checker, SMC4AC, developed and implemented to automate the verification of interaction among intelligent agents. SMC4AC is the result of developing a new symbolic model checking algorithm devoted to CTLCα, a combination of CTL and new temporal modalities to represent and reason about conditional commitments and common commitment actions. The core of this paper consists of a new logical language, a detailed description of the symbolic algorithms needed for commitments and their action modalities, complexity analysis, implementation and application. The implementation of our algorithm and its graphical user interface is built on top of the MCMAS symbolic model checker tailored for checking intelligent multi-agent systems. We select business processes and multi-agent interaction protocols as application domains to test and validate the effectiveness and scalability of SMC4AC. We report extensive experimental results, which confirm the theoretical findings and make SMC4AC practical. [ABSTRACT FROM AUTHOR]