Relations

Relations in situation theory can be treated as objects. In barsit, Jon Barwise states:

Relations are the glue that holds things together, the primary constituents of the facts that go to make up reality. Any relation we use in the theory can also be objectified and treated as an object of the theory.

As in first order logic, every relation $R$ has arguments. Since situation theory is designed to capture information about reality, restrictions on the kind of arguments certain relations can take have to be imposed. Barwise takes a notion of appropriateness between relations and the objects, that can serve as their arguments, as given. In later versions of situation theory, roles take this place.

There is no reason to assume, that the arguments are in a predefined order. Therefore an assignment is a function $a$ assigning objects to some arguments of the function. It is not necessary to fill all argument places with objects. Although it is convenient for us to assume, that all argument places are filled by appropriate objects, there is no reason to justify such a step. Consider the relation of eating. This relation takes at least three arguments: the eater $E$, the food eaten, $F$, and a space-time-location $t$ where the eating takes place. Let $eating(E,F,t)$ be this relation. However, even if we do not know the food eaten, $F$, it still makes sense to issue a statement, that $E$ is eating at $t$. The classic approach to this statement in logic would be the proposition $\exists x \left(eating(E,x,t) \right)$. If we want to model information expressed in natural language, there is no reason to state $\exists x \left(eating(E,x,t) \right)$ from the sentence ``$E$ is eating at $t$''. We take an assignment $a$ filling only the role of the eater and the space-time-location, and leaving the food unassigned: $eating(E,x,t)$, or sometimes $eating(E,t)$.