Optimal Fixed-Premise Repairs of EL TBoxes

Support for a partitioning of the ontology into a static part and a refutable part. Improvement of FP-repairs by selective, automatic introduction of new premises (can currently be done manually).


Introduction
Related Work: Classical Repairs, Gentle Repairs, Countermodel Repairs Optimal Fixed-Premise Repairs Conclusion and Outlook

Repairs
An ontology can contain axioms that are incorrect in the underlying domain, especially if it was constructed from incomplete data or using inexact methods based on machine learning. Such errors are detected when a reasoner generates faulty consequences. Goal: Repair the ontology for these unwanted consequences.

Repairs
An ontology can contain axioms that are incorrect in the underlying domain, especially if it was constructed from incomplete data or using inexact methods based on machine learning. Such errors are detected when a reasoner generates faulty consequences. Goal: Repair the ontology for these unwanted consequences. My paper focuses on repairing EL TBoxes. A hitting set of all justifications for P is still needed to construct a gentle repair, but now all axioms in it are weakened according to a weakening relation ≻. A weakening relation ≻ sub for EL concept inclusions: Problems:

Related Work: Countermodel Repairs
The unwanted consequences in P are entailed since no counterexamples were known during the construction of the TBox T .
A model containing such counterexamples can now be obtained from the user or be constructed automatically. The TBox is then rewritten according to the countermodel.

Repair-by-Countermodel Approach:
Axiomatize the logical intersection of the TBox and a countermodel.
F. Kriegel: Constructing and extending description logic ontologies using methods of formal concept analysis. Doctoral thesis (2019) Advantage: Axiomatization method is very precise and thus produces repairs that retain large amounts of knowledge. Disadvantage: Repairs are often large (and cannot be made smaller).

Generalized-Conclusion Repairs
Inspired by the gentle repairs w.r.t. ≻ sub as well as by the countermodel repairs, and in order to tackle their problems, a novel type of repairs is introduced. A generalized-conclusion repair (GC-repair) T ′ of T is a repair such that additionally:

Generalized-Conclusion Repairs
Inspired by the gentle repairs w.r.t. ≻ sub as well as by the countermodel repairs, and in order to tackle their problems, a novel type of repairs is introduced. A generalized-conclusion repair (GC-repair) T ′ of T is a repair such that additionally: Canonical construction of GC-repairs: 1 Choose a polynomial-size repair seed S. 2 Construct the induced countermodel J S . 3 Replace each concept inclusion C ⊑ D with C ⊑ D ∨ C J S J S . Main result: For each TBox and each repair request, the set of all optimal GC-repairs can be computed in exponential time, and every GC-repair is entailed by an optimal one.

Fixed-Premise Repairs
As seen in the last example, GC-repairs might not be satisfactory. We thus define: A fixed-premise repair (FP-repair) T ′ of T is a repair that satisfies the following additional condition: For each C ′ ⊑ D ′ ∈ T ′ , there is C ⊑ D ∈ T such that C = C ′ .

Fixed-Premise Repairs
As seen in the last example, GC-repairs might not be satisfactory. We thus define: A fixed-premise repair (FP-repair) T ′ of T is a repair that satisfies the following additional condition: For each C ′ ⊑ D ′ ∈ T ′ , there is C ⊑ D ∈ T such that C = C ′ . FP-repairs can be computed by a little modification to the framework for GC-repairs. Main result: For each TBox and each repair request, the set of all optimal FP-repairs can be computed in exponential time, and every FP-repair is entailed by an optimal one. Contrary to GC-repairs, optimal FP-repairs might need additional expressivity.
(But this is no problem!)

Conclusion
A novel approach to repairing EL TBoxes for unwanted concept inclusions has been developed. Two variants: GC-repairs and FP-repairs Each optimal repair is characterized by a polynomial-size repair seed. Optimal repairs can be computed in exponential time. Prototypical implementation: https://github.com/francesco-kriegel/ right-repairs-of-el-tboxes