Generalized Earley Deduction and Its Correctness

This paper describes a deduction method that works both top-down and bottom-up. The method can be viewed as an extension of a well-known approach|Earley deduction|to handle negation-as-failure. We show that with respect to the stratiied model theory of 1] the method is sound, that it is strongly complete (terminating) for function-free programs with negation, and complete for programs without negation if function symbols are allowed. The method uses the call graph of a program to represent static dependencies, and a Truth Maintenance System to store dynamic dependencies between partial lemmas generated by the deduction method. We argue by means of examples that these dependencies allow the method to avoid some redundant deductions, and that they are useful in forward reasoning in the presence of negation-as-failure.