A Superposition Calculus for Abductive Reasoning

TL;DR

This paper introduces a modified superposition calculus tailored for abductive reasoning, which is proven sound and complete, and terminates for many theories relevant to SMT, enhancing logical consequence generation.

Contribution

It presents a novel superposition calculus modification that guarantees soundness, completeness, and termination for abductive reasoning in first-order logic with finite ground terms.

Findings

Proven soundness and deductive completeness with redundancy rules.

Ensures termination for many SMT-relevant theories.

Applicable to generating consequences from first-order axioms.

Abstract

We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules, provided the considered consequences are built on a given finite set of ground terms, represented by constant symbols. In contrast to other approaches, most existing results about the termination of the superposition calculus can be carried over to our procedure. This ensures in particular that the calculus is terminating for many theories of interest to the SMT community.