Within the broad area of knowledge pattern science, an important topic is the discovery, description, and evaluation of modeling patterns for a certain task. One of the most controversial problem is constituted by modeling relations with large or variable (polymorphic) arity. There is indeed a large literature on representing n-ary relations in logical languages with expressivity limited to unary and binary relations, e.g. when time, space, roles and other knowledge should be used as indexes to binary relations. In this paper we provide a comparison of several design patterns, based on their respective (dis)advantages, as well as on their axiomatic complexity. Data on actual processing time for queries and DL reasoning from an in-vitro study is also provided.
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