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Modeling Personal Identifiable Information using First-Order Logic

Estimating the quality of Personal Identifiable Information (PII) creates a corresponding need to model and formalize PII for both the real-world and electronic data, in a way that supports rigorous reasoning relative to real-world constraints, rules from domain experts, and rules about expected data patterns. In this paper, we propose an extended first-order logic language (FOL), called PDFOL (Person Data First-order Logic), that can express these kinds of constraints and rules, as well as relevant person attributes and inter-person relations. We present the salient features of PDFOL, namely temporal predicated based on time intervals, aggregate functions, and tuple-set comparison operators. These features allow PDFOL to model person-centric databases, enabling formal and efficient reason about their quality. We show how PDFOL can express real-world constraints, expert opinions, and aggregate knowledge as closed PDFOL statements, which in turn can then be used to assess the quality of a database. We adapt and extend the traditional aggregate functions in three ways: a) allowing any arbitrary number free variables in function statement, b) adding groupings, and c) defining new aggregate function. We believe that this work will provide a foundation for future methods for reasoning about the quality of PII.