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Onto-Med >> Theories >> GFO Part I Basic Principles

 
   


10.1 Relations, Relators and Relational Roles

Let us first consider the connection between a relation and its arguments (referring to facts on an intuitive basis). At this point, a particular fact seems to involve a relation and particular arguments. John's being a patient of hospital $A$ is one fact, while the same John's being a patient of hospital $B$ amounts to a different fact. Different particular arguments are involved in these facts, but the same relationship appears, namely ``being a patient of''. For this reason we assume that relations exhibit a categorial character.24

As a consequence, we must identify the instances of a relation. In contrast to the extensional definition of relations in a mathematical reading, we do not consider the mere collection of the arguments with respect to a single fact, as an instance of a relation. For example, the pair $(John, hospital A)$ is not an instance of the relation ``being a patient of''. Instead, we assume that there are individual entities with the power of connecting other entities (of any kind). These connecting entities are called relators or relation individuals, and they are the instances of a relation. Relators themselves offer an ``internal'' structure that allows one to distinguish the differences between the way in which the arguments of a relation participate in a fact. Returning to the example, John is involved differently in the fact of being a patient of hospital $A$, as is the hospital. Exchanging John and the hospital would result in a strange sentence like ``the hospital $A$ is a patient of John''. We say that John and the hospital play different roles in that relationship. Formally, this leads us to the introduction of an additional type of entity: relational roles25. A relator can be decomposed into relational roles, such that each role is a mediator between exactly one argument and the relator.

Now, the link between an argument and a relator can be completed. The relationship between relators and roles is called role-of. As indicated in (37,36), role-of might be understood as a subtype of an abstract part-of relationship (namely between roles and relators), but we will not adopt this definition until a sound standing comparison of the role-of and part-of relations is available. Further, roles must be connected with the relata of the relator. This purpose is served by the basic relation plays. It is then subsumed by the basic relation dependent-on, because roles are a specific kind of dependent entity: they are dependent on their player (which is the relatum) and on complementary roles (such that the totality of involved roles constitutes the relator).

Robert Hoehndorf 2006-10-18
 
       
     
     
     

   
     
     
       
 

deutsch   imise uni-leipzig ifi dep-of-formal-concepts