# Towards a Hybrid Approach to Context Reasoning for Underwater Robots
## 5 The Proof of Concept: A Case Study on Oil Spill Detection
### Context Reasoning in the Case Study
#### 5.3.3 MEBN Reasoning  
An MEBN model, shown in Figure 6, is built using the UnBBayes tool to reason about the severity level of spills under uncertainties. The MEBN model is formatted in an OWL format and stored in the context reasoner. Figure 6: The Multi-Entity Bayesian Network (MEBN) model to reason about the severity level of spills. The MTheory consists of seven MFrags, _Thickness_, _EstimatedSize_, _Wearther_, _Currents_, _Location_, _SpreadSpeed_, and _SeverityLevel_. Each MFrag represents knowledge for a specific entity and its local probability distribution. Specifically, the _Thickness_, _EstimatedSize_, _Wearther_, _Currents_, and _Location_ MFrags provide modeling of variable _Thickness_, EstimatedSize, Weather, Currents, and Location and their prior probability distribution. The _SpreadSpeed_ and _SeverityLevel_ MFrags represent local probability distribution of variable _SpreadSpeed_ and _SeverityLevel_ under the influence of their causal variables, such as _Weather_, _Currents_, and _Thickness_. For instance, the _SpreadSpeed_ MFrag models that the spread speed of detected spills is affected by two inputs, namely, Weather and Currents. These two input nodes, weather and currents, are specified in the _Weather_ and _Currents_ MFrags, respectively. The local probability distribution of _SpreadSpeed_ is shown in Figure 7. Annotation of this probability information using PR-OWL constructs can be seen in Figure 8. In this case study, all the probability information in this model is directly provided by marine experts based on their experiences. It is worth noting that the probability information can also be derived from historical data. With the aforementioned seven MFrags, the MTheory could collectively model the unique joint probability distribution for the SeverityLevel entity. The MTheory represents an infinite number of possibilities, thus it can be instantiated to specific scenarios and inferences made based on the observed evidence. In this scenario, the obtained findings are listed in Figure 9. As shown in Figure 9, all necessary context information for estimating the severity level of the spilled region is obtained. Figure 8: Ontology annotation of SpreadSpeed local probability distribution. Figure 7: The local probability distribution of SpreadSpeed. With the complete findings specified in Figure 9, the MEBN can be specified to the scenario and instantiated as a SSBN, as shown in Figure 10.  
Based on standard BN inferences, the SSBN can be queried to find updated beliefs of different random variables. For example, the region_1 with the existence of two spills could be estimated as very serious with a probability of 88% and there is a 90% chance that the spread speed of spill_1 and spill_2 will be fast. This high-level context could be sent to the MMT for further exploitation. For instance, it could be used by operators as a parameter to conceive a plan for underwater robots so that they can take remedial measures accordingly. It is also worth noting that the MEBN reasoning can reason under  
Figure 10: Situation-Specific Bayesian Network (SSBN) generated for the scenario with complete findings. Figure 9: Findings in the scenario. incomplete and uncertain contexts. For instance, in the same scenario, assuming that the thickness of two spills is unknown, the nodes in the MEBN model can be collectively instantiated as an SSBN to represent the specific scenario. The newly generated SSBN with incomplete findings can be seen in Figure 11. As shown in Figure 11, the instantiated nodes of Thickness, namely, Thickness_spill_1 and Thickness_spill_2, are not populated with evidence. However, even with unknown contexts, SSBN can also make inferences under uncertainties. The severity level of the spilled region can be inferred with as high a probability as 78.24%. It is a fact that this estimation is less reliable than the previous inference with complete findings known.