# Inconsistency Proofs for ASP: The ASP-DRUPE Format

## TL;DR

This paper introduces ASP-DRUPE, a new proof format for verifying inconsistency in Answer Set Programming, based on RUP, with correctness proof and implementation in the wasp solver.

## Contribution

It develops ASP-DRUPE, a novel proof format for ASP inconsistency, adapting RUP for logic programs, and demonstrates its integration and correctness.

## Key findings

- ASP-DRUPE is correct and sound.
- Implemented in the wasp solver.
- Facilitates formal verification of ASP inconsistency.

## Abstract

Answer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs. This work is under consideration for acceptance in TPLP.