Simplifying Negative Goals Using Typed Existence Properties

A method for extracting positive information from negative goals is proposed. It makes use of typed existence properties between arguments of a predicate to rewrite negative goals in a logic program. A typed existence property is a generalization of functional dependencies in that an input value maps to a fixed number of output values. Types are used to specify the domains of the input and output values. An implementation of the simplification method is presented and its complexity is analyzed. A key algorithm of the implementation checks if an atom in a negative goal can be extracted using a given typed existence property. A digraph links an atom to the quantified variables occurring in the atom and is used to quickly retrieve atoms in the negative goal that may become extractable after some other atom is extracted.