Abstract: According to the status of temporal logic languages without object-oriented concepts, projection temporal logic is extended, and then the new syntax and semantics are introduced. In the extended projection temporal logic, formal definitions of objects, classes, and inheritances are given based on the hierarchical variable sets and grouping predicates. An object-oriented temporal logic language framed tempura++, is defined as an executable subset of extended projection temporal logic, and it can be used for object-oriented programming and simulating the execution of composite web services. The illustrated example shows that the language can reuse code efficiently and improve code readability and maintainability in compare with Framed Tempura.