Linking temporal first-order logic with Bayesian networks for the simulation of pervasive computing systems

The authors’ previous work discussed a scalable abstract knowledge representation and reasoning scheme for Pervasive Computing Systems, where both low-level and abstract knowledge is maintained in the form of temporal first-order logic (TFOL) predicates. Furthermore, we introduced a novel concept of a generalised event, an abstract event, which we define as a change in the truth value of an abstract TFOL predicate. Abstract events represent real-time knowledge about the system and they are defined with the help of well-formed TFOL expressions whose leaf nodes are concrete, low-level events using our AESL language.In this paper, we propose to simulate pervasive systems by providing estimated knowledge about its entities and situations that involve them. To achieve this goal, we enhance AESL with higher-order function predicates that denote approximate knowledge about the likelihood of a predicate instance having the value True with respect to a time reference. We define a mapping function between a TFOL predicate and a Bayesian network that calculates likelihood estimates for that predicate as well as a confidence level, i.e., a metric of how reliable the likelihood estimation is for that predicate.Higher-order likelihood predicates are implemented by a novel middleware component, the Likelihood Estimation Service (LES). LES implements the above mapping; first, for each abstract predicate, it learns a Bayesian network that corresponds to that predicate from the knowledge stored in the sensor-driven system. Once trained and validated, the Bayesian networks generate a likelihood estimate and a confidence level. This new knowledge is maintained in the middleware as approximate knowledge therefore providing a simulation of the pervasive system, in the absence of real-time data. Last but not least, we describe an experimental evaluation of our system using the Active BAT location system.