Another Generic Setting for Entity Resolution: Basic Theory

Benjelloun et al. \cite{BGSWW} considered the Entity Resolution (ER) problem as the generic process of matching and merging entity records judged to represent the same real world object. They treated the functions for matching and merging entity records as black-boxes and introduced four important properties that enable efficient generic ER algorithms. In this paper, we shall study the properties which match and merge functions share, model matching and merging black-boxes for ER in a partial groupoid, based on the properties that match and merge functions satisfy, and show that a partial groupoid provides another generic setting for ER. The natural partial order on a partial groupoid is defined when the partial groupoid satisfies Idempotence and Catenary associativity. Given a partial order on a partial groupoid, the least upper bound and compatibility ($LU_{pg}$ and $CP_{pg}$) properties are equivalent to Idempotence, Commutativity, Associativity, and Representativity and the partial order must be the natural one we defined when the domain of the partial operation is reflexive. The partiality of a partial groupoid can be reduced using connected components and clique covers of its domain graph, and a noncommutative partial groupoid can be mapped to a commutative one homomorphically if it has the partial idempotent semigroup like structures. In a finitely generated partial groupoid $(P,D,\circ)$ without any conditions required, the ER we concern is the full elements in $P$. If $(P,D,\circ)$ satisfies Idempotence and Catenary associativity, then the ER is the maximal elements in $P$, which are full elements and form the ER defined in \cite{BGSWW}. Furthermore, in the case, since there is a transitive binary order, we consider ER as ``sorting, selecting, and querying the elements in a finitely generated partial groupoid."