The Temporal Logic of Rewriting

This paper presents the temporal logic of rewriting TLR∗. Syntactically, TLR∗ is a very simple extension of CTL∗ which just adds action atoms, in the form of spatial action patterns, to CTL∗. Semantically and pragmatically, however, when used together with rewriting logic as a “tandem” of system specification and property specification logics, it has substantially more expressive power than purely state-based logics like CTL∗, or purely action-based logics like A-CTL∗. Furthermore, it avoids the system/property mismatch problem experienced in state-based or action-based logics, which makes many useful properties inexpressible in those frameworks without unnatural changes to a system’s specification. The advantages in expresiveness of TLR∗ are gained without losing the ability to use existing tools and algorithms to model check its properties: a faithful translation of models and formulas is given that allows verifying TLR∗ properties with CTL∗ model checkers. Simulations and bisimulations reflecting and/or preserving useful classes of TLR∗ properties are also studied. Finally, a strategy language for rewriting is used as a way to verify (resp. falsify) guarantee (resp. safety) formulas in TLR∗ for infinite-state systems and, more generally, to verify strategy formulas about such systems using semidecision procedures.