The ``Supports'' relation

We introduce a binary relation between states of affairs and situoids, $\models \subseteq Situoid \times Infon$. If $s$ is a situoid and $\phi$ an infon, $\models (s,\phi)$ reads ``$\phi$ obtains in the situoid $s$. We will use infix notation for this relation: $s \models \phi$, and write $s \not\models \phi$ for $\neg s\models (s,\phi)$.

With the help of this relation, we can say what we mean by a fact of a situoid.

Definition 5.12 (Fact)   An infon $\phi$ is a fact, $\models \phi$, if and only if there is a situoid $s$, such that $s \models \phi$. If $s \models \phi$, $\phi$ is called a fact of $s$.

The first part of this definition may be ambiguous. Infons contain a pictural state of affairs and a function, mapping this picture to 0 or $1$. Because there has to be a state of affairs, that corresponds to the picture, the infon has to correspond to a state of affairs in some world. One could argue, that this state of affairs would have to be part of some situoid. Since situoids have to fulfill more conditions than merely being a part of reality, it is unclear at this stage of this thesis, if there are states of affairs that are not part of any situoid, and we will not give an answer here.

The second part of the definition is apparently more clear, and we will constantly use it. Situoids, as special parts of the world, are comprehended, and then infons are asserted to obtain in situoids. If an infon $\phi$ with polarity $p$ is a fact of the situoid $s$, then the state of affairs $x$ with $corr(\phi,x)$ is present in $s$ if $p=1$, and it is not present in $s$ if $p=0$.