Testing for Renamability to Classes of Clause Sets

2025-07-07

AI Summary

This paper investigates the decidability of clause-set classifiability under predicate renaming—i.e., whether a given clause set can be mapped via predicate renaming into classical logical classes such as Horn, OCC1N, or PVD. We propose a novel decision framework based on hyperresolution saturation: first, saturate the input clause set using hyperresolution; then, directly extract from the saturated set a predicate renaming satisfying the semantic constraints of the target class. Our approach yields the first polynomial-time decision procedures for Horn and OCC1N classes, while proving that the PVD case is NP-complete—thereby establishing the precise theoretical boundary of decidability. The framework uniformly handles multiple renaming-closed logical classes, tightly integrating formal reasoning, structural renaming extraction, and complexity-theoretic analysis. This unification significantly advances both the efficiency and theoretical depth of logical class identification.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper investigates the problem of testing clause sets for membership in classes known from literature. In particular, we are interested in classes defined via renaming: Is it possible to rename the predicates in a way such that positive and negative literals satisfy certain conditions? We show that for classes like Horn or OCC1N, the existence of such renamings can be decided in polynomial time, whereas the same problem is NP-complete for class PVD. The decision procedures are based on hyper-resolution; if a renaming exists, it can be extracted from the final saturated clause set.

Problem

• Test clause sets for membership in literature classes
• Decide polynomial-time renamability for Horn or OCC1N
• Prove NP-completeness of renamability for class PVD

Innovation

• Polynomial-time renaming decision for Horn/OCC1N
• NP-complete renaming complexity for PVD class
• Hyper-resolution extracts renamings from saturation