RI: Small: Knowledge Representation and Reasoning under Uncertainty with Probabilistic Answer Set Programming

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Combining logic and probability is an important subject in Artificial Intelligence, and is recently being extensively studied in the area of statistical relational learning, where the main goal of representation is to express probabilistic models in a compact way that reflects the relational structure of the domain and ideally supports efficient learning and inference. However, in comparison with main knowledge representation languages, such languages do not allow natural, elaboration tolerant representation of commonsense knowledge. Currently, there is a big gap between the state of the art languages that are used in knowledge representation and the state of the art languages in which machine learning is done. The success of this project will identify fundamental issues in bridging the gap between the two areas, will produce a uniform framework for both expressive representation and learning, and will contribute to the integration of knowledge representation and machine learning. The outcome of the research will be useful for many applications that require integration of knowledge representation and other areas, such as vision, robotics, and event recognition, where commonsense reasoning has to be applied on uncertain knowledge and data. The software systems developed under this project will be freely available as open source software. The research will involve both graduate and undergraduate students, contributing to a strengthened relationship between education and research. The goal of the project is to design and implement a knowledge representation language that allows elaboration tolerant representation of expressive commonsense knowledge involving logic and probability, which can be efficiently computed by the techniques developed in related areas. The proposed research aims at shifting the current logic-based foundation of answer set programming to a novel foundation that combines logic and probability, and achieving its computation by intelligently adapting and combining the methods from probabilistic reasoning and machine learning. It will build upon the existing works on answer set programming, statistical relational learning, and probabilisitic logic programming. The project will (i) enhance the mathematical foundation of answer set programming to the novel foundation that combines logic and probability. (ii) relate it to other existing approaches in statistical relational learning, Pearl's causal models, and P-Log; (iii) design inference and learning algorithms; (iv) design a high level action language that allows elaboration tolerant representation of probabilistic transition systems; (v) apply probabilistic answer set programming to event recognition; (vi) implement and evaluate involved software systems.