The Temporal Logic of Rewriting: A Gentle Introduction

Abstract

This paper presents the temporal logic of rewriting $\mathit{TLR}^{\ast}$. Syntactically, $\mathit{TLR}^{\ast}$ is a very simple extension of $\mathit{CTL}^{\ast}$ which just adds action atoms, in the form of spatial action patterns, to $\mathit{CTL}^{\ast}$. 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 $\mathit{CTL}^{\ast}$, or purely action-based logics like A-$\mathit{CTL}^{\ast}$. 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 $\mathit{TLR}^{\ast}$ 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 $\mathit{TLR}^{\ast}$ properties with $\mathit{CTL}^{\ast}$ model checkers.