Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies
Abstract
:1. Introduction
 A set of XML tags identifying abnormalities and context;
 A set of algorithms for manipulating the tags and applying the adaptive proofs to OWL ontologies;
 A validation from different usecases of ontology contextualization.
2. Related Work
2.1. Preliminaries
2.2. Dealing with Change and Inconsistencies
2.3. Expression of Context in Ontologies
2.4. Adaptive Logics
 $\mathsf{\Gamma}\subseteq C{n}_{\mathbf{LLL}}\left(\mathsf{\Gamma}\right)$ (Reflexivity)
 If ${\mathsf{\Gamma}}^{\prime}\subseteq C{n}_{\mathbf{LLL}}\left(\mathsf{\Gamma}\right)$ then $C{n}_{\mathbf{LLL}}\left({\mathsf{\Gamma}}^{\prime}\right)\subseteq C{n}_{\mathbf{LLL}}\left(\mathsf{\Gamma}\right)$ (Transitivity)
 Adds premises to the theory
 Infers rules at some conditions or unconditionnally
 Retracts (mark) rules or reintegrates (unmark) rules into the theory
3. Expressing Context and Dealing with Inconstistencies Using Adaptive Logics
3.1. Expressing AL Elements in DL: Adaptive Context Expression (ACE)
3.2. Reasoning on ACE Elements (RACE)
 It can cause an inconsistency in A. If that is the case, some rules in A must be marked and go into $\epsilon $. As a consequence;
 Some rules in E may become valid regarding their abnormalities toward the rules in A now that some rule in A has been marked. If this is the case, then the said rules should go from $\epsilon $ to A and another run of verifying if the new rule in A may cause inconsistency is necessary, and so on until no more rules are added in A.
4. Expressing ACE Abnormalities
4.1. Expressing an Abormality on a Specific Rule
4.2. Expressing Conjunctions and Disjunctions in Abnormalities
4.3. Expressing the Set of Abnormalities $\mathsf{\Omega}$
5. Experiments
5.1. Preliminaries
 An output ontology ACEn.owl_AceVerified.owl (when testing ontology ACEn.owl);
 A log file named ace.log.
5.2. Tests Description and Results
Algorithm 1: RACE minimal abnormality strategy 
Ensure : The resulting ontology is consistant

Algorithm 2: RulesMarking algorithm 
Ensure : After the integration of a new rule in A, every $(a,\mathsf{\Lambda})\in A$ remains valid regarding its set of abnormalities $\mathsf{\Lambda}$.

Algorithm 3: RulesUnmarking Algorithm 
Ensure : After the integration of a new rule in A, every $(a,\mathsf{\Lambda})\in E$ should remain marked regarding its set of abnormalities $\mathsf{\Lambda}$.

5.3. Basic Tests
5.4. Testing $\mathsf{\Omega}$
5.5. Advanced Testing: Order of Appearance of Formulas in the Knowledge Base, Marking and Unmarking, Conjunctions and Disjunctions
6. Summary of the Tests
 F1: $magnitude:SeismCharacteristics$
 F2: $\neg (geophysics:Context)$
 F3: $geophysics:Context$
 F4: $astrophysics:Context$
 F5: $\neg (astrophysics:Context)$
 F6: $magnitude:StellarParameters$.
7. Conclusions and Future Works
 Alignment between the ontologies to merge needs to be ensured before the merging.
 Complex abnormalities (e.g., $a\wedge (b\vee (\neg c\vee d\left)\right)$) can be tricky to express.
 The order in which formulas, related to other formulas’ abnormalities, are encountered somewhat matters. A formula, unbound to any abnormality and part of (more than one) other formula abnormality, may induce a precedence of one formula toward another. This is shown in the tests using ACE6.owl. Apart from this specific case, the order in which formulas and abnormalities are encountered does not matter.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Tested in  $\mathsf{\Omega}$  $({\mathit{a}}_{1},{\mathit{\lambda}}_{1})$  $({\mathit{a}}_{2},{\mathit{\lambda}}_{2})$  Source  Unmarked 

ACE1.owl    F1,F2       
ACE2.owl    F1,F2    F3  F1 
ACE3.owl    F1,F2  F6,F5  F3 F5  F1 
ACE4.owl  F3∧F4  F1,F2  F6,F5  F3 F4  F1 
ACE5.owl  F3∧F4  F1,F2  F6,F5  F3 F4  F1 
ACE6.owl  F3∧F4  F1,F2  F6,F5  F3 F4  F6 
ACE7.owl    F6,F5∨F2    F3 F4  F6 
ACE8.owl    F6,F5∨F2    F4   
ACE9.owl  F3∧F4  F6,F5∨F2    F4 F3  F4 
ACE10.owl  F3∧F5  F1,F2  F6,F5  F4 F3  F6 F1 
ACE11.owl  F3∧F5  F1,F2  F6,F5  F3   
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Louge, T.; Karray, M.H.; Archimède, B. Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies. Information 2022, 13, 139. https://doi.org/10.3390/info13030139
Louge T, Karray MH, Archimède B. Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies. Information. 2022; 13(3):139. https://doi.org/10.3390/info13030139
Chicago/Turabian StyleLouge, Thierry, Mohamed Hedi Karray, and Bernard Archimède. 2022. "Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies" Information 13, no. 3: 139. https://doi.org/10.3390/info13030139