diff --git a/2-state-of-the-art/state-of-art.tex b/2-state-of-the-art/state-of-art.tex index 6d5e64e..8b30e6a 100644 --- a/2-state-of-the-art/state-of-art.tex +++ b/2-state-of-the-art/state-of-art.tex @@ -161,31 +161,28 @@ primary assurance evidence remain as significant challenges. Formal verification of any system requires a precise language for stating what the system must do. Temporal logic provides this language by extending classical propositional logic with operators that express properties over -time. Where propositional logic can state that a condition is true or false, -temporal logic can state that a condition must always hold, must eventually -hold, or must hold until some other condition is met. This expressiveness -makes temporal logic the foundation for specifying reactive systems---systems -that continuously interact with their environment and must satisfy ongoing -behavioral requirements. - -For nuclear control applications, temporal logic captures exactly the kinds -of properties that matter: safety properties (``the reactor never enters an -unsafe configuration''), liveness properties (``the system eventually reaches -operating temperature''), and response properties (``if coolant pressure -drops, shutdown initiates within bounded time''). These properties can be -derived directly from operating procedures and regulatory requirements, -creating a formal link between existing documentation and verifiable system -behavior. - -NASA's Formal Requirements Elicitation Tool (FRET) bridges the gap between -natural language requirements and temporal logic specifications. FRET -provides a structured intermediate language that allows engineers to define -temporal behavior without writing raw logic formulas. The HARDENS project -used FRET for requirement capture, and it has been validated on aerospace -systems including a Lift+Cruise aircraft with 53 formalized -requirements~\cite{Pressburger2023}. FRET's ability to start with imprecise -natural language and iteratively refine it into well-posed specifications -makes it particularly suited to formalizing nuclear operating procedures. +time~\cite{baier_principles_2008}. Where propositional logic can state that +a condition is true or false, temporal logic can state that a condition must +always hold, must eventually hold, or must hold until some other condition is +met. Linear temporal logic (LTL) formalizes these notions through four key +operators: +\begin{itemize} + \item $\mathbf{X}\phi$ (next): $\phi$ holds in the next state + \item $\mathbf{G}\phi$ (globally): $\phi$ holds in all future states + \item $\mathbf{F}\phi$ (finally): $\phi$ holds in some future state + \item $\phi \mathbf{U} \psi$ (until): $\phi$ holds until $\psi$ becomes + true +\end{itemize} +These operators allow specification of safety properties ($\mathbf{G}\neg +\text{unsafe}$), liveness properties ($\mathbf{F}\text{target}$), and +response properties ($\mathbf{G}(\text{trigger} \rightarrow +\mathbf{F}\text{response})$). For nuclear control, this expressiveness +captures exactly the kinds of requirements that matter: the reactor must +never enter an unsafe configuration, the system must eventually reach +operating temperature, and if coolant pressure drops, shutdown must initiate +within bounded time. These properties can be derived directly from operating +procedures and regulatory requirements, creating a formal link between +existing documentation and verifiable system behavior. \subsubsection{Differential Dynamic Logic}