Probability is nowadays the state-of-the-art approach to handle uncertainty. Important, efficient and elegant frameworks for representing and reasoning with probabilistic models include Bayesian networks, hidden Markov models, stochastic context-free grammers, etc. They all have been applied to important real-world problems in diagnosis, forecasting, automated vision, sensor fusion, manufacturing control, speech recognition, and computational biology. However, these traditional approaches have one major drawback: they have a rigid structure and therefore have problems representing a variable number of objects and general relations among objects. Consider e.g. building a probabilistic models of a class of computer networks with Bayesian networks. This is problematic because the complex and dynamic structure of computer networks, and the relations among their different components, cannot elegantly be modeled using Bayesian networks. Indeed, it is quite likely that the structure of different networks is at an abstract level quite similar. However, using Bayesian networks each computer network would need to be modeled by its own specific Bayesian network. There is no way of formulating general probabilistic regularities for all the computer networks. Furthermore, whenever components are added or deleted to a computer network its corresponding Bayesian network should be modified. This in turn would lead to exponential updating problems.
To overcome these limitations, various researchers have recently proposed logical extensions of classical probabilistic models incorporating the notions of objects and relations into them (see. Moreover, a surprising array of techniques have been developed in the past decade for learning such probabilistic models. One can approach probabilistic-logical models and learning such models from various sides as there are three underlying domains: probability, logic, and learning. E.g. various techniques for probabilistic learning gradient-based methods, the family of EM algorithms or Markov Chain Monte Carlo methods have been developed and exhaustively investigated in different communities, such as in the Uncertainty in AI community for Bayesian networks and in the Computational Linguistic and the Computational Biology communities for Hidden Markov Models. These techniques are not only theoretically sound. Inductive Logic Programming has studied logic learning, i.e. learning and data mining within first order logic representations. Inductive Logic Programming has significantly broadened the application domain of data mining especially in bio- and chemoinformatics and now represent some of the best-known examples of Scientific Discovery by AI systems in the literature. However, traditional techniques only focus on (at most) two of the three underlying domains. No clear understanding of the relative advantages and limitations of different probabilistic-logical model (learning) techniques has yet emerged.