Axiom Dynamics 7: Large-Scale Machine Checking of a Lightweight Terminological Ontology for the Deadlock Criterion on Real Rule Bases

Lightweight terminological ontologies are usually implemented as fragments ofHorn rule systems, whose axiom sets are required in practice to be consistent andincrementally maintainable. This paper examines the execution criterion of axiomtransitions within the candidate space of leaf-premise single-antecedent rules: givena baseline rule system and a candidate batch, the question is whether there exists an ordering of the batch such that, when the candidates are applied one byone, every step produces a nonempty newly added object-level derived pair. Underthe conditions that the baseline derivation relation is acyclic, candidate premisesare leaves, and candidate rules have single antecedents, the blocking relation constitutes a strict partial order among distinct candidates; under the condition thatthe batch has no inter-candidate chain, the folding lemma guarantees that everymulti-hop derivation contains a single-hop blocker, whence every batch without aninter-candidate chain admits a legal sequential execution, and a legal order is explicitly constructed in polynomial time as a linear extension of the blocking partialorder; when a chain exists this construction may fail, and its existence is registeredas an open problem. The semantics of proper subfamilies with equivalent closure istherefore located as ledger-redundancy declaration internal to a batch, rather thanas a criterion for sequential infeasibility. At the quantitative level, when there is nointer-candidate chain the batch gain equals the union of the candidate tail sets, andcoverage enumeration agrees with the general formula under this condition; whena chain exists the coverage formula may omit bridging pairs, and this boundaryis fixed by a strict synthetic counterexample. Machine checking on four real OBOcorpora registers the zero-redundancy reading of the single-axiom redundancy survey, the negative result of candidate-pool scale and equivalence-class compressionratio 1.0, and, on a 12-candidate demonstration batch, the reading of the inclusionminimal redundancy-declaration subfamily obtained by running all 4096 subsets.The theoretical conclusions hold within the boundaries of the Horn fragment, leafpremises, single antecedents, and an acyclic baseline; the sequential-feasibility conclusion additionally requires that the batch have no inter-candidate chain; universaldirectional propositions are borne by proofs, while machine checking bears finitecounterexample search and implementation cross-verification.