aiqbench analysis
This paper presents a theoretical framework for generating minimum-cost evidence certificates in Horn reasoning systems that remain valid even when up to $k$ source domains fail. By utilizing rule-closed counterinterpretations, the authors avoid computationally expensive enumeration of failure scenarios while proving coNP-completeness for unrestricted verification and offering tractable solutions under specific reachability restrictions. The work addresses critical robustness challenges in automated reasoning and knowledge representation, particularly relevant for building reliable AI systems dependent on multiple data sources.
Minimum-Cost Robust Evidence Certificates for Horn Reasoning under Correlated Source Failures
arXiv:2610.25865v1 Announce Type: new Abstract: A small justification for a rule-based conclusion may disappear when a source is withdrawn, and multiple derivations need not provide independent evidence. We study minimum-cost certificates that preserve a Horn conclusion under every withdrawal of at most k source domains. Evidence records remain distinct from asserted facts, supporting replicated attestations and overlapping failure dependencies. Transversals of minimal-support footprints characterize robustness and explain why disjoint-proof requirements can reject valid certificates. An exact procedure alternates weighted evidence selection with a source-failure oracle. A rule-closed counterinterpretation yields a globally valid selection cut without enumerating supports or failure scenarios. We prove correctness, finite termination, and cost optimality, establish coNP-completeness of unrestricted verification and NP-completeness of synthesis for every fixed budget, and identify a tractable reachability restriction. Experiments on controlled benchmarks, reachability graphs, and ontology-derived instances demonstrate that our counterinterpretation-guided synthesis achieves up to 92% optimum coverage within practical resource bounds, outperforming scenario expansion and general abduction while confirming the necessity of transversal-based reasoning over proof-packing heuristics.
Abstract:A small justification for a rule-based conclusion may disappear when a source is withdrawn, and multiple derivations need not provide independent evidence. We study minimum-cost certificates that preserve a Horn conclusion under every withdrawal of at most k source domains. Evidence records remain distinct from asserted facts, supporting replicated attestations and overlapping failure dependencies. Transversals of minimal-support footprints characterize robustness and explain why disjoint-proof requirements can reject valid certificates. An exact procedure alternates weighted evidence selection with a source-failure oracle. A rule-closed counterinterpretation yields a globally valid selection cut without enumerating supports or failure scenarios. We prove correctness, finite termination, and cost optimality, establish coNP-completeness of unrestricted verification and NP-completeness of synthesis for every fixed budget, and identify a tractable reachability restriction. Experiments on controlled benchmarks, reachability graphs, and ontology-derived instances demonstrate that our counterinterpretation-guided synthesis achieves up to 92% optimum coverage within practical resource bounds, outperforming scenario expansion and general abduction while confirming the necessity of transversal-based reasoning over proof-packing heuristics.
Artificial Intelligence (cs.AI)
I.2.4; I.2.3; F.4.1
arXiv:2610.25865 [cs.AI]
(or arXiv:2610.25865v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2610.25865 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 257 words