Aligning real-world ontology pairs often requires establishing complex correspondences, as conceptual di erences between them may be too profound to bridge with simple equivalence correspondences. Yet, most ontology alignment algorithms are restricted to nding simple equivalences between ontology entities. This work presents a suite of novel algorithms for Complex Ontology Alignment (COA) that rely on a targeted application of Association Rule Mining (ARM) to known complex alignment patterns. This approach reduces the ARM search space, and enables the application of tailored semantic ltering algorithms for re ning the mappings. We evaluated our approach using a pattern-oriented manual method, which yielded a global weighted precision of 75%, but revealed our approach was unable to nd mappings for some of the patterns present in the reference. On the other hand, our approach found several mappings for patterns not present in the reference with high weighted precision, highlighting the importance of establishing evaluation metrics that consider varying degrees of correctness while being fully automated.
Ontology alignment is critical to address the semantic heterogeneity problem, as it nds correspondences that enable integrating data across the Semantic Web. One of its biggest challenges is that ontology schemas often di er conceptually, making it necessary to establish complex correspondences. A complex correspondence is an ontology mapping where at least one of the mapped entities is an expression, rather than a simple ontology entity. The expressions used in complex mappings include restrictions (e.g. 8x; y; o1 : M arriedP erson(x) o2 : hasSpouse(x; y) ^ o2 : P erson(y)) and constructions using logical operatores (e.g. 8xo1 : M other(x) o2 : P arent(x) ^ o2 : W oman(x)).
The relevance of the Complex Ontology Alignment (COA) sub- eld has been
acknowledged by the Ontology Alignment Evaluation Initiative (OAEI) 1 who
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Commons License Attribution 4.0 International (CC BY 4.0).
1 http://oaei.ontologymatching.org
introduced a Complex track in 2018 [
ARM exploring a shared set of instances is a promising approach. However, the fact that we have prior knowledge of the complex alignment patterns we want to nd makes it ine cient to use a \catch-all" ARM algorithm to perform an exhaustive search for frequent itemsets, and only use the knowledge of the patterns a posteriori to lter the rules. Therefore, we propose to invert this paradigm, by using prede ned complex alignment patterns to guide ARM. This e ectively reduces the search space and allows the application of semantic-based ltering algorithms tailored to each kind of pattern, to select and re ne the most relevant mappings. 2
Our ontology alignment approach consists of the following steps: 1. An initial ontology loading step retrieves the set of shared individuals between the two ontologies and organises the ontology information (types, relations and property values of each individual, ranges and domains of the properties and hierarchical relations between classes) in hash-tables. 2. For each complex alignment pattern, an individual pattern matching algorithm iterates through the set of shared individuals, and, for each individual, it searches the hash-table data structures containing the relevant data for the targeted alignment pattern. For each mapping candidate found, we increment the support (i.e., the frequency) of the source and target entities in the mapping and the support of the mapping itself (i.e., the fraction of shared individuals that have both the source and target entities). 3. A common ARM matching algorithm is then invoked by each pattern matching algorithm to lter mapping candidates by support and con dence, therefore extracting association rules. 4. Filtering algorithms select which of the candidate mappings to include in the nal alignment, excluding redundant mappings and con icting mappings with lower con dence. An aggregator algorithm combines mappings for the same entity into a single mapping using logical operators, such as \AND" and \OR".
Our algorithms cover eight distinct complex patterns, from which seven were found in the cmt conf erence dataset (see Table 1). Additionally, they can produce combinations of these patterns through disjunction and conjunction. 3
We integrated our algorithms in the ontology matching system AMLC [
Correct [1.0]: The mapping is formally correct (regardless of whether it is present in the reference alignment).
Nearly correct [0.75]: Only minor corrections necessary (e.g., alter the mapping relation type or substitute a class for its sub- or super-class). Plausible [0.5]: The mapping seems sensible and no information in the ontologies or reference alignment contradicts it.
Implausible [0.25]: The mapping seems incorrect and is likely derived from biases in the dataset, but no information in the ontologies or reference alignment contradicts it.
False [0.0]: The mapping is contradictory to the reference alignment and/or ontologies.
Our approach allows for ne tuning of matchers and lters, speci c to each pattern, yielding precise results (Table 1). While it was unable to nd mappings for some of the patterns present in the reference, it found several mappings for patterns not present in the reference with high weighted precision. 4
We developed a novel complex ontology matching method based on
patternguided ARM, which represents a paradigm shift by making used of the alignment
patterns to steer, rather than lter, the ARM process. Our manual evaluation
revealed that the majority of mappings we found are correct or nearly correct, even
if not present in the reference alignment. These results highlight the importance
of establishing evaluation metrics that consider varying degrees of correctness
while being fully automated. Going forward we will investigate the
computational performance of our approach versus classical ARM, and extend the types
of patterns it captures.
2 Available at: http://oaei.ontologymatching.org/2020/complex/index.html#
popconf; Reference alignments provided by Thieblin et al. [