da Costa and Tarski meet Goguen and Carnap: a novel approach for ontological heterogeneity based on consequence systems

Domain ontologies require review against knowledge recorded in evolving external resources. We propose COATER, a method that manages executable review components called arrows. Each arrow compares a scoped part of an ontology with a relevant resource and reports support or challenges to its axioms. Challenges may prompt proposals for completion, correction, or restructuring and become tasks for human or agent-assisted triage. Per-axiom coverage summarizes the assessments. We illustrate COATER with the FSL ontology in software language engineering (SLE): arrows review language coverage, language conceptualization, and software-engineering activities. An LLM-assisted linkage exercise increases compliance with a defined Wikipedia-linkage policy from 405 to 600 of 600 entities. A structured catalogue of SLE resources organizes review opportunities.

Decidability or complexity issues about the consistency problem for description logics with concrete domains have already been analysed with tableaux-based or type elimination methods. Concrete domains in ontologies are essential to consider concrete objects and predefined relations. In this work, we expose an automata-based approach leading to the optimal upper bound EXPTIME, that is designed by enriching the transitions with symbolic constraints. We show that the nonemptiness problem for such automata belongs to EXPTIME if the concrete domains satisfy a few simple properties. Then, we provide a reduction from the consistency problem for ontologies, yielding EXPTIME-membership. Thanks to the expressivity of constraint automata, the results are extended to additional ingredients such as inverse roles, functional role names and constraint assertions, while maintaining EXPTIME-membership, which illustrates the robustness of the approach

The Isabelle/HOL dataset of Benzmüller and Scott's study of Gödel's ontological argument and Scott's variant (Monatshefte für Mathematik, 2025) is carried to Lean 4 and from there back to the automated provers, as a benchmark independent of either proof assistant. The port covers all thirty theories, structure and names preserved: 548 statements compare identical as parsed, every named result is proved again, and five results the original reports without replaying them are proved here. For every theorem, #print axioms gives the postulates its proof consumes: Scott's necessary existence and modal collapse need only a symmetric frame, confirming that KB suffices. The benchmark, in TPTP THF and SMT-LIB, turns the steps of an argument debated in philosophy into 294 theorems, alongside 45 statements the original refutes or leaves open, ten left open there. Five THF provers, and cvc5 on SMT-LIB, prove 227 theorems within ten seconds on one core and 232 within sixty, and none proves any of the 45. E and Leo-II solve the most, although Leo-II's calculus has been unchanged for about a decade and was only repaired and modernised here, as release 2.2. Vampire, whose later version won the higher-order division of CASC-30, solves the most in no configuration. Only E and Leo-II are measured in their own automatic mode: Zipperposition proves 101 in a single mode and 213 with its developers' portfolio, Vampire 174 without options and 209 with a higher-order schedule that its CASC mode does not select, and Leo-III 159 alone and 177 with E as partner.