Anchors

Situations as well as situoids are instances of at least one universal. Universals are intensional, they determine the properties of its instances. Unfortunately, we have no means of describing those properties, and the language GOL does not provide those means either. Because there is no plausible formalism how to specify universals, we will develop one ourselves, but just for situations and situoids. This may be generalized to other categories, but we will not take our approach that far.

Before we do this, we have to change our perspective a bit. While we have been concerned with ontological properties of situations, situoids, infons and states of affairs until now, we will need to focus more on formal details of those entities than we have done before. We omitted those details because they were not relevant in our previous discussion.

Remember that relations in the General Formal Ontology are special types of universals. Instances of those universals are called relators. Every relation $R$ comes with a set of argument roles, $Arg(R)$. For example, the relation $eating$ comes with the role of the $eater$, the $eaten$, and the $location$ the eating takes place. Those roles are filled with objects of appropriate sort. The $eater$ has to be some kind of living organism, the $eaten$ some physical entity, the $location$ a spatio-temporal one, specified by a chronoid or time-boundary and a topoid. An instance of the relation universal, the relator, connects entities of appropriate sort. The connection between those individual objects through the relator is what we called a state of affairs. Pictural states of affairs are determined by an instance of a relation $R$, the relator $r$, and an assignment function assigning appropriate objects to the set of arguments of $R$, $Arg(R)$. The assignment function may be partial. Let $R$ be a relation, $f$ the assignment function and $\{x_1,...,x_i,...,x_n\}$ be the set of arguments of the relation $R$ in the pictural state of affairs $\phi=\langle\langle R,...,x_i,...\rangle\rangle$. Then $\langle\langle R,...,x_i,...\rangle\rangle [f]=\langle\langle R,...,f(x_i),...\rangle\rangle$. Sometimes, in situation theory, this function $f$ is called an anchor.

We will use a similar notion for infons. Let $i$ be an infon with the pictural state of affairs $\phi=\langle\langle R,x_1,...,x_i,...,x_n\rangle\rangle$. Let $f$ be an assignment function: $f: \{x_1,...,x_n\} \mapsto Entity$. Then $f$ satisfies the infon $i$ relative to a situation $s$ iff $s \models i[f]$ iff $s\models i'$ and $f$ is the assignment function of the pictural state of affairs of $i'$. Because we will need the assignment function more often in the future, we introduce the following definition.

Definition 5.28 (Anchor function)   Let $i$ be an infon with the pictural state of affairs $\phi$, and let $f$ be the assignment function that is part of $\phi$. Then $anchor(i)=f$.