Two ontology design patterns in the domain of collections

Collections are objects used to arrange, into a single unit, multiple data items that form a natural group. Different types of collections exist, due to different constraints based on whether or not they impose an order on their elements and whether or not they allow repetition of elements. Any of them are easily found in several domains of our everyday life. For instance, a deck of cards, the prime divisors of a number or the teams that compete in a championship can be seen as a collection. Thus, an effective modeling of collections is a recurring issue in information management. In the ontology design field, recurring modeling problems can be addressed by the use of Ontology Design Patterns (ODPs). In the case of collections, ODPs have been proposed for representing sequences, lists, sets and bags. However, none of these patterns are completely adequate for representing collections of ordered elements without repetition. In this paper we present an ODP for representing that notion, which we have named Permutation . Moreover, another ODP named ListOfPermutations is also introduced, which allows to represent how the order of a Permutation varies along time. Because not all constraints required by these ODPs can be represented in OWL 2, SHACL shapes have been used in their definitions. • ODP Permutation for representing ordered collections without repetition. • ODP ListOfPermutations for representing ordered permutations of the same elements. • Use of SHACL to define constraints of the proposed ODPs not representable in OWL 2.