Extending Real Logic with Aggregate Functions
IJCLR-2021, NeSy Workshop
Real Logic is a recently introduced first-order language where formulas have fuzzy truth values in the interval [0, 1] and semantics are defined concretely with real domains. The Logic Tensor Networks (LTN) framework has applied Real Logic to many important AI tasks through querying, learning, and reasoning. Motivated by real-life relational database applications, we study adding aggregate functions, such as averaging elements of a relation table, to Real Logic. The key contribution of this paper is the formalization of such functions within Real Logic. This extension is straightforward and fits coherently in the end-to-end differentiable language that Real Logic is. We illustrate it on FooDB, a food chemistry database, and query foods and their nutrients. The resulting framework combines strengths of descriptive statistics modeled by fuzzy predicates, FOL to write complex queries and formulas, and SQL-like expressiveness to aggregate insights from data tables.
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