# SWARMs Ontology: A Common Information Model for the Cooperation of Underwater Robots
## 2 Related Work
### Existing Solutions for Modeling Uncertainties  
The W3C UR3W-XG group [25] proposed an ontology of uncertainty which captures top-level classes and properties for characterizing the uncertainty consideration in ontologies. Uncertainty that might exist in ontologies is classified into five main types: _ambiguity_, _randomness_, _vagueness_, _inconsistency_, and _incompleteness_. Different mathematical theories could be used to deal with different types of uncertainty reasoning: fuzzy logic, Bayesian network (BN), Markov logic network, etc. In order to model different kinds of uncertainty and further provide support for uncertainty reasoning, several attempts have been followed. For instance, [PERSON] et al. [26] introduced fuzzy logic in crisp ontologies to capture and represent vagueness of uncertain information. They proposed to model fuzzy ontology elements (e.g., fuzzy data types, fuzzy concepts, and fuzzy modifiers) by using the Web Ontology Language (OWL) 2 annotations. Probability is the best-known formalism for computational uncertainty reasoning, particularly effective for addressing randomness, inaccuracy, and incompleteness of uncertain information. While introducing uncertainty in knowledge representation languages has been an afterthought, it is common to use simple XML tags to express the probability value which is a number ranging from 0 to 1. However, this is just one simple aspect of probabilities. Probability has been regarded by many authors to be more about structure than it is about numbers. For instance, to model uncertainty from a probabilistic aspect and enable the ease of applying BN reasoning, [PERSON] et al. [27] proposed a probability-annotation approach. Specifically, three ontology concepts, including \"PriorProb\", \"CondProb\", and \"FullProbDist\", were defined to conceptualize collections of Bayesian related definitions. In addition, a data property \"ProbValue\" was proposed to link \"PriorProb\" and \"CondProb\" with the probabilistic value varying from 0 to 1. BN is effective to model and reason a fixed number of hypotheses. However, it cannot reason problems which involve a varying number of entities. To address this shortcoming of BN, Multi-Entity Bayesian Network (MEBN) [28], as an extension of standard BN, was proposed by [PERSON] et al. The PR-OWL ontology [29], which complies with the MEBN theory, was also proposed to annotate probability information about uncertain context. The MEBN could be very effective in reasoning problems in the presence of uncertainties with a varying number of entities involved. The approach of using the PR-OWL ontology to annotate uncertainty information in ontologies and provide support for MEBN reasoning has been adopted in many applications, such as procurement fraud detection [30], maritime awareness [31], and knowledge-driven analysis for cultural heritage [32]. As addressing context uncertainty, particularly focusing on its inaccuracy, incompleteness, and randomness features, this paper will firstly introduce the use of PR-OWL to annotate probability information and further provide support for MEBN reasoning over uncertainties in the underwater robot field. Incorporated with ontology constructs defined in the PR-OWL ontology, the proposed SWARMs ontology can properly model uncertainties and provide a complete representation for the coordination and cooperation of underwater vehicles. In addition, the probability-annotated SWARMs ontology can provide support for a hybrid context reasoning mechanism, including ontological, rule-based, and MEBN reasoning.