Inconsistency Proofs for ASP: The ASP - DRUPE Format

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.

Advanced tools and methods for treewidth-based problem solving

“…This resulted in several proof formats for solvers deciding satisfiability [Gelder, 2008;Goldberg and Novikov, 2003] and further problem formalisms [Heule et al, 2013;Wetzler et al, 2014;Heule et al, 2014;Lonsing and Egly, 2018b]. In the light of these works, the resulting initiative on explainability for artificial intelligence, and a recent proof logging format adapted for answer set programming [Alviano et al, 2019b], it might be interesting to consider applying and adapting such formats for the algorithms of Chapter 3 or further approaches based based on dynamic programming.…”

Inconsistent Cores for ASP: The Perks and Perils of Non-monotonicity

“…An unsatisfiable core of a given program Π is a subset C of literals that make the program Π ∪ {← ¬ℓ | ℓ ∈ C} under the (literal) assumptions C inconsistent. Besides core-guided optimization, assumptions and unsatisfiable cores are relevant for cautious reasoning (Alviano et al 2018b), explainability (Alviano et al 2019), belief revision (Garcia et al 2018), and forgetting rules (cf. Gonc ¸alves, Knorr, and Leite 2021).…”