# MEBN-RM: A Mapping between Multi-Entity Bayesian Network and Relational Model
###### Abstract  
Multi-Entity Bayesian Network (MEBN) is a knowledge representation formalism combining Bayesian Networks (BNs) with First-Order Logic (FOL). MEBN has sufficient expressive power for general-purpose knowledge representation and reasoning, and is the logical basis of Probabilistic Web Ontology Language (PR-OWL), a representation language for probabilistic ontologies. Developing an MEBN model to support a given application is a challenge, requiring definition of entities, relationships, random variables, conditional dependence relationships, and probability distributions. When available, data can be invaluable both to improve performance and to streamline development. By far the most common format for available data is the relational database (RDB). Relational databases describe and organize data according to the Relational Model (RM). Developing an MEBN model from data stored in an RDB therefore requires mapping between the two formalisms. This paper presents MEBN-RM, a set of mapping rules between key elements of MEBN and RM. We identify links between the two languages (RM and MEBN) and define four levels of mapping from elements of RM to elements of MEBN. These definitions are implemented in the MEBN-RM algorithm, which converts a relational schema in RM to a partial MEBN model. Through this research, the software has been released as an MEBN-RM open-source software tool. The method is illustrated through two example use cases using MEBN-RM to develop MEBN models: a Critical Infrastructure Defense System and a Smart Manufacturing System. Both systems are proof-of-concept systems used for situation awareness, where data coming from various sensors are stored in RDBs and converted into MEBN models through the MEBN-RM algorithm. In these use cases, we evaluate the performance of the MEBN-RM algorithm in terms of mapping speed and quality to show its efficiency in MEBN modeling. m 2019 9 1743 23 April 2019 26 April 2019 2019 12 March 2019 23 April 2019 26 April 2019 2019 2019 20  
LOGic [11], Markov Logic Networks [12], Conditional Random Fields for Logical Sequences [13], Bayesian Logic Programming [14], FACTORIE: Probabilistic Programming [15], and Probabilistic Conditional Logic [16]. Multi-Entity Bayesian Network (MEBN) belongs to the formalisms in SRL. MEBN is a knowledge representation language based on Bayesian Networks (BN) [17] and First-Order Logic (FOL). MEBN is sufficiently expressive for general-purpose knowledge representation and reasoning in an uncertain and complex world. Because MEBN is flexible enough to represent a variety of complex and uncertain situations, it has been applied to systems for Predictive Situation Awareness (PSAW), the problem of understanding and predicting aspects of a temporally evolving situation [18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. In a recent review of knowledge representation formalisms, [PERSON] et al. [28] recommended MEBN as having the most comprehensive coverage of features needed to represent complex problems among several Artificial Intelligence (AI) models including statistical RMs. The reviewed formalisms included MEBN, Hidden Markov Models [29], Artificial Neural Networks [30], BNs [17], Support Vector Machine [31], Fuzzy BNs [32], Dynamic BNs [33], Probabilistic RMs [1], and Markov Logic Networks [12]. Also, MEBN has been applied to a wide variety of domains [34]. Construction of relational structures (e.g., FOL and RM) for MEBN is an active research topic. Probabilistic Web Ontology Language (PR-OWL) [35] extends the Web Ontology Language (OWL) to represent uncertainty. A domain ontology, typically represented in a relational language, provides common semantics for expressing information about entities and relationships in a domain. PR-OWL is an upper ontology, written in OWL, that uses MEBN to express uncertainty about entities and relationships in an OWL ontology. PR-OWL 2 extends PR-OWL to provide better integration with OWL [36]. [PERSON] et al. [37] provides a methodology for developing MEBN theories expressed as PR-OWL ontologies.