Extensions of standard Z refinement relation for multiple viewpoints oriented requirements method

The authors extend the standard Z refinement relation for the multiple viewpoint oriented requirements method (MVORM). The original motivation is that we found the standard Z refinement to be inadequate or incorrect when considering specifications that have temporal relationships of operations. We do our work under a generic framework of MVORM. The concept of temporal state variables is introduced into Z. Then, new implementation relations are defined and new refinement relations are deduced, mainly process temporal relationships of operations. We use a state transition system to abstract temporal state transitions. A simple example is used to show the usage of MVORM.