Subsumption checking

The resulting synthesis mechanism is then as follows (we here omit aspects related to the detection of potential non-termination, which may arise due to the semidecidability of subsumption checking). 

Subsumption checking deduces whether subsumption relations can be established between ontology classes based on their definitions. 

The fourth step takes all pairs of nodes and computes a semantic relationship matrix based on the positioning of nodes within their own ontologies. Semantic relations are translated into propositional connectives, with equivalence being translated into equivalence, subsumption into implication, and disjointness into negation. Then, the following formula is checked for satisfiability ... 

OWL DL is an expressive language that is a fragment of FOL. This means that it is amenable to machine reasoning. Ontologies described in OWL DL can be checked for logical consistency and subsumption hierarchies (the lattice of is-a links) inferred from the descriptions of classes formed from the links made between classes [20,24,25]. This form of OWL is the focus of this section. 

Lines 7 and 8 check if the states reachable in one step are included in the sets of states found in the previous iterations. This is done by using the prune-by-subsumption operation PbySwhich removes from N those paths which are instances of some paths in R. This operation uses syntactic matching between terms that label two corresponding nodes to find such paths. If the result is the empty set, then the procedure terminates and reports success. Otherwise, the Mdg Q represents the new frontier set. 

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