Trust model is an important component of gird security model and can be classified as mission-unaware identity trust model, mission-aware identitytrust model, mission-unaware behavior trust model and mission-aware behavior trust model. All of them could be regarded as projections of missionaware behavior trust model, by which authorization depends on not only the trust but also the cost and quantity of the mission. This paper proposes a formal description of this trust model by using abstract state machine (ASM). It will facilitate us understanding its semantics and accurate definitions, and bridging the gaps between de facto industry standards and this trust model. These formalizations are vertical refinements of the ASM based ground model for grids and could be easily jointed on it.