A Superposition Calculus for Abductive Reasoning
This work addresses the need for efficient abductive reasoning in automated theorem proving, particularly for SMT applications, though it is incremental as it builds on existing superposition calculus results.
The authors tackled the problem of generating consequences from first-order axioms by modifying the superposition calculus, resulting in a sound and deductive-complete approach that is terminating for many theories relevant to SMT.
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.