# Reasoning about Confidence in Goal Satisfaction
## 2 Background  
In this paper, we use URN's GRL to represent concerns and requirements as goals in a graphical form in order to facilitate understanding and communication with various stakeholders. Figure 1 presents the main elements of GRL including goals, softgoals, tasks, resources, indicators, and the links connecting these elements (AND/OR/XOR decompositions of, contributions to and dependencies among goals). The User Requirements Notation includes, in addition to GRL, a process notation called Use Case Maps (UCM), and various traceability links can be created and exploited between GRL and UCM views, e.g., goal-process alignment. Actors represent systems and stakeholders, and carry intentions represented by the other GRL elements [4]. Goals are often used to capture high-level functional requirements that can be fully met, whereas softgoals are mainly capturing more quality-oriented aspects related to non-functional requirements (e.g., increased security). Tasks show activities or solutions considered. These model elements may have dependencies on various resources. Indicators (also known as Key Performance Indicators--KPIs) convert observable values in a given unit (e.g., Euro or km/h) to a GRL satisfaction value by comparing it to target, threshold, and worst-case parameters. These elements will be further illustrated in the case study (Section 6), but their nature does not really influence how confidence levels are computed in this paper. GRL provides analysis techniques that help to resolve and highlight inconsistencies, incompleteness, or conflicts in requirements. The language also shows trade-offs, enabled by GRL strategies (i.e., sets of initial values), among stakeholder intentions. Propagation algorithms are used to propagate the satisfaction values of leaf goals through links to root goals. Satisfaction values are computed using initial satisfaction values of leaf goals and weights/types of links [4]. Satisfaction values can be qualitative (e.g., help, hurt, make, break) or quantitative, e.g., on a scale from 0 (dissatisfied, with the GRL element color-coded in red to 100 (satisfied, color-coded in green). For values in between, different shades of orange, yellow (for the neutral value 50), and chartreuse are used; the greener the better, and the redder the worse. Figure 2 explains the different labels that accompany a sample GRL model with two tasks initialized in a strategy, with the propagated satisfaction level. The \(\mathcal{C}[k]\) and DQ[\(k\)] labels are not part of the standard language but are new types of labels proposed in this paper. [PERSON] et al. [5] formalized the standard propagation algorithm using arithmetic equations that express how the propagated satisfaction values (\(v(\ldots)\)) are computed based on the  
Figure 1: Syntax of GRL’s modeling elements. Figure 2: Explanation of standard and new GRL labels used in this paper. type of GRL links connecting the GRL elements (this time independently of their type that is presented in Figure 1):
* _AND-Decomposition_: the minimum satisfaction value of sub-goals is propagated (see Figure 3), as expressed in Equation (1); \[v(S)=Min(v(D_{1}),v(D_{2}),\ldots,v(D_{n})),\] (1) where \(v(S)\) is the satisfaction value of the decomposed source GRL element and \(v(D_{x}),1\leq x\leq n\) are the satisfaction values of the decomposing GRL elements (i.e., the destinations of the decomposition link). In Figure 3, and others like it, note the color coding that reflects the satisfaction level of each element, as discussed earlier. In addition, in the jUCM Nav tool used to produce these evaluated GRL models [3], the GRL elements that are initialized in a strategy are shown with (*) next to the quantitative satisfaction value, and with the element contour displayed with a dashed line. The other model elements have satisfaction values computed (using propagation rules) from initialized or already computed elements.