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Perceptron Operators That Count

The Felony Score Sheet used in the US State of Florida, describes various features of a crime and their assigned points. Features may include ‘possession of cocaine’, or ‘number of caused injuries’. A threshold must be reached to decide compulsory imprisonment. In previous research, we have introduced a perceptron operator for knowledge representation languages. With it, concepts can be defined by listing a concept’s features with associated weights, and a threshold. An individual belongs to such a concept if the weighted sum of the listed features it belongs to reaches the threshold. It can capture the concept of compulsory imprisonment defined by the Felony Score Sheet. However, it suffers some limitations in that one must artificially use concepts like ‘caused one injury’, ‘caused two injuries’, etc, to be able to count. This paper proposes an extension of the perceptron operator to define concepts like the compulsory imprisonment from the Felony Score Sheet faithfully and easily, relying on role-successors counting. We show that when the weights are non-negative, reasoning in ALC augmented with the perceptron operator can be reduced to reasoning in ALCQ. Capitalizing on the recent ALCSCC, we also show that adding the operator to ALC does not affect the complexity of reasoning in general.