# Ontological Approach for Automatic Inference of Concrete Crack Cause
## 3 Ontology for Automatic Inference of Crack Cause
### Semantic Reasoning and Query  
The crack location, penetration, complexity, regularity, shape, exposure/corrosion, leak/efflorescence information obtained through visual inspection is recognized as one of the crack types and is recommended for the \"crack type ontology\" as appropriate for the crack type.  
For example, the attribute information of cracks such as \"Slab_Bottom_Center, Surface Penetration, Complexity, Regularity, Grid Shape, Exposure/Corrosion, and Leak/Efflorescence\" is parsed and automatically recognized in the classes of \"Crack Location, \"Penetration\", \"Complexity\", \"Regularity\", \"Shape\", \"Exposure/Corrosion\", or \"Leak/Efflorescence\" as an instance. The attribute information of the recognized cracks is recognized as an instance (CT_1) of lower class called \"CrackType_1\" with the following necessary and sufficient conditions: Slab_Bottom_Center, Surface Penetration, Complexity, Regularity, Grid Shape, Exposure/Corrosion, and Leak/Efflorescence among the lower classes of \"Crack Type Class\" through inference. Next, the crack cause of \"CrackType_1\" is the most appropriate crack cause to the crack type \"CT_1\" among the lower classes of \"Crack Cause Class\" whose necessary condition is \"A2(Material-Used Material-Cement-Heat of Hydration of Cement), A9(Material-Concrete-Shrinkage of Concrete), B12(Construction-Steel-Arrangement of Steel-Lack of Cover)\", which eventually diagnoses the crack cause.  
For this inference process, the rules of inference must be defined. In this study, various documents [2; 6; 8], including the specifications of the Ministry of Land, Infrastructure, and Transport [7], were reviewed and in-depth interviews were conducted with three experts  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Object Property** & **Domain** & **Range** \\ \hline Has Crack Location & Crack Type & Crack Location \\ Has Penetration & Crack Type & Penetration \\ Has Complexity & Crack Type & Complexity \\ Has Regularity & Crack Type & Regularity \\ Has Shape & Crack Type & Shape \\ Has Exposure/Corrosion & Crack Type & Exposure/Corrosion \\ Has Leak/Efflorescence & Crack Type & Leak/Efflorescence \\ Has Crack Type & Crack Cause & Crack Type \\ Has Crack Cause & Crack Type & Crack Cause \\ \hline \hline \end{tabular}
\end{table}
Table 5: Definition of properties.  
with more than 25 years of working experience in crack diagnosis. The rules of reasoning, which reflect the results of the literature review and interview, are as follows:  
CT_1 \(\equiv\)  
Necessary and Sufficient  
\(\
i\) hasCrackLocation has Slab_Bottom_Center  
\(\
i\) hasPenetration has Surface  
\(\
i\) hasComplexity has Complex  
\(\
i\) hasRegularity has Regularity  
\(\
i\) hasShape has Grid  
\(\
i\) hasExposure/Corrosion has No_Exposure/Corrosion  
\(\
i\) hasLeak/Efflorescence has Leak/Efflorescence  
Necessary  
\(\
i\) hasCrackType has A2  
\(\
i\) hasCrackType has A9  
\(\
i\) hasCrackType has B12  
The validation and reasoning of the ontology utilized HermiT Reasoner ver.1.4.3.456, contained in Protege v5.5.0. Validation shows that the ontology is defined consistently without logical errors on its own and that property information defining the crack type in the lower class of \"CrackType_1\" is recognized correctly (see Figure 3).  
The ontology implemented using the DL Query included in Protege v5.5.0 allows the inference of crack types with the properties of crack types (see Figure 4) and allows the inference of crack causes from crack types (see Figure 5). In other words, if the RDF format contains property information that can determine the class of ontology, it means that the crack type is recognized through the inference process, and the crack cause corresponding to the crack type is recognized.  
Figure 3: Verification results.