# Introduction¶

**Relations** are entities that glue together other entities. Every relation has a number of **relata** as arguments, which are connected or related by it. The number of a relation’s arguments is called its arity. As much as an unary property such as *being Red,* properties of higher arities such as *being married-to, being heavier-than* are universals, since they can be predicated of a multitude of individuals. Relations can be classified according to the types of their relata. There are relations between sets, between individuals, and between universals, but there are also cross-categorical relations, for example, between urelements and sets or between sets and universals. We divide relations into two broad categories, called Material and Formal relations. *Formal relations* hold between two or more entities directly without any further intervening individual. Examples of formal relations are:

- 5 is
*greater than*3 - this day
*is part of*this month - N is
*subset of*Q

but also the relations of instantiation, inherence, quale of a quality, association, existential dependence, among others – … relations that form the mathematical superstructure of our framework. *Material relations,* conversely, have material structure on their own and include examples such as:

- employments
- kisses
- enrollments
- flight connections
- commitments

The relata of a material relation are mediated by individuals that are called relators. Relators are individuals with the power of connecting entities:

*a flight connection,*for example, founds a relator that connects airports*an enrollment*is a relator that connects a student with an educational institution

**Quoted from:**

GUIZZARDI, Giancarlo. *Ontological Foundations for Structural Conceptual Models.* Enschede: CTIT, Telematica Instituut, 2005.