From model space to aDCSP

Once the model space has been constructed, it can be translated into an aDCSP. The translation procedure, summarised as algorithm $\CALL{createaDCSP}{\mbox{}}$, consists of three steps as described below:

1. Generate the attributes and domain values from the assumptions. The aDCSP attributes correspond to the underlying assumption classes (i.e. groups of assumptions indicating alternative choices with regards to the same model construction decision). A relevance assumption and its negation jointly form an assumption class. For example, $A_1=${(relevant growth frog), $\neg$(relevant growth frog)} specifies such an assumption class. The set of model assumptions involving the same participants/relations, but with different model names and hence different descriptions, also form an assumption class. For instance, $A_2=${(model $\texttt{n}_{\text{frog}}$ exponential), (model $\texttt{n}_{\text{frog}}$ logistic), (model $\texttt{n}_{\text{frog}}$ other)}, where $\texttt{n}_{\text{frog}}$ is a variable denoting the size of a population, specifies such an assumption class. Running this step of the algorithm, an attribute is created for each assumption class, with the domain of such an attribute consisting of all assumption instances in the assumption class.
2. Create activity constraints. The attributes and domain values generated in the previous step are only meaningful in situations where the participant and/or relation instances contained in the arguments of the corresponding assumptions exist. For example, the assumption (model $\texttt{n}_{\text{frog}}$ logistic) is only relevant if the participant instance $\texttt{n}_{\text{frog}}$ exists. Clearly, all assumptions within one assumption class have the same participant and/or relation instances as their arguments. Because each assumption class corresponds to one attribute, the attribute can be activated if and only if the participant and/or relation instances associated with the related assumption class are active. Therefore, this step creates activity constraints that activate an attribute based on the conjunction of the environments contained within the labels of the participants/relations of the assumption class. For instance, as can be deduced from Figure 7, $\texttt{n}_{\text{frog}}$ is activated when (relevant growth frog) is committed. Thus, the attribute corresponding to assumption class $A_2$, defined in step 1, is activated under the attribute value assignment associated with the (relevant growth frog) assumption.
3. Create compatibility constraints. In the ATMS (or model space), all sources of inconsistencies are contained in the label of the nogood node. Therefore, the compatibility constraints are created directly by translating the environments in the label ${\cal L}(\bot)$ into the corresponding conjunctions of attribute-value assignments.