deletions | additions       diff --git a/The_formal_models_of_ontologies__.tex b/The_formal_models_of_ontologies__.tex  index 91c4c38..58bc128 100644  --- a/The_formal_models_of_ontologies__.tex  +++ b/The_formal_models_of_ontologies__.tex 
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2d stage: redefining the subnet obtained at the first stage. To implement this stage the semantic rules were formulated to search the additional resources on the base of current learner competencies, and search the auxiliary resources, as well as the rules for defining the logical links between learning resources in personal collection. Auxiliary resources are the resources which are not included in the set of additional resources because of too long learning sequence but these resources can help to get the missing competences which are not provided by the set of additional resources.  The developed set of semantic rules allows to create the personal learning collection in accordance with the learning outcomes, current knowledge level and other preferences of the learner. This collection includes the relations between the learning resources to manage the learning process. To represent the ontology reasoning rules for learning resources retrieval and integration we used SWRL language. SWRL extends the OWL-DL and is based on first-order predicate calculus that allows to represent the reasoning rules as a set of Horn clauses.   Below are a few examples of semantic rules. The SWRL-rule for learning resources retrieval based on the preferred language has the following form:  \begin{multline}\label{eq5}  COL:hasStudent(?c, ?u) \wedge L:hasLanguage(?u,?l) \wedge \\