Development of agent systems is without question a complex task when autonomous, reactive and proactive characteristics of agents are considered. Furthermore, internal agent behavior model and interaction within the agent organizations become even more complex and hard to implement when new requirements and interactions for new agent environments such as the Semantic Web are taken into account. We believe that the use of both domain specific modeling and a Domain-specific Modeling Language (DSML) may provide the required abstraction and support a more fruitful methodology for the development of Multi-agent Systems (MASs) especially when they are working on the Semantic Web environment. Although syntax definition based on a metamodel is an essential part of a modeling language, an additional and required part would be the determination and implementation of DSML constraints that constitute the (formal) semantics which cannot be defined solely with a metamodel. Hence, in this paper, formal semantics of a MAS DSML called Semantic Web enabled Multi-agent Systems (SEA_ML) is introduced. SEA_ML is a modeling language for agent systems that specifically takes into account the interactions of semantic web agents with semantic web services. What is more, SEA_ML also supports the modeling of semantic agents from their internals to MAS perspective. Based on the defined abstract and concrete syntax definitions, we first give the formal representation of SEA_ML's semantics and then discuss its use on MAS validation. In order to define and implement semantics of SEA_ML, we employ Alloy language which is declarative and has a strong description capability originating from both relational and first-order logic in order to easily define complex structures and behaviors of these systems. Differentiating from similar contributions of other researchers on formal semantics definition for MAS development languages, SEA_ML's semantics, presented in this paper, defines both static and dynamic aspects of the interaction between software agents and semantic web services, in addition to the definition of the semantics already required for agent internals and MAS communication. Implementation with Alloy makes definition of SEA_ML's semantics to include relations and sets with a simple notation for MAS model definitions. We discuss how the automatic analysis and hence checking of SEA_ML models can be realized with the defined semantics. Design of an agent-based electronic barter system is exemplified in order to give some flavor of the use of SEA_ML's formal semantics. Lessons learned during the development of such a MAS DSML semantics are also reported in this paper.