Simplifying Negative Goals Using Typed Existence Properties

TL;DR

This paper introduces a method to simplify negative goals in logic programs by leveraging typed existence properties, which generalize functional dependencies and utilize types to efficiently extract positive information.

Contribution

It presents a novel approach using typed existence properties to rewrite negative goals, along with an implementation and complexity analysis.

Findings

The method effectively extracts positive information from negative goals.

The implementation includes a key algorithm for atom extraction based on typed existence properties.

Complexity analysis demonstrates the approach's efficiency.

Abstract

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.