Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the incorporation of background knowledge, which can be very useful in domains where prior knowledge from experts is available and can lead to a more data-efficient learning regime. Be that as it may, the limitation to Horn clauses composed over Boolean variables is a very serious one. Many phenomena occurring in the real-world are best characterized using continuous entities, and more generally, mixtures of discrete and continuous entities. In this position paper, we motivate a reconsideration of inductive declarative programming by leveraging satisfiability modulo theory technology.
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