Compound infons

There are three kinds of compound infons, the meet of a set of infons and the existentialization of an infon respectively an argument $x$, and the negation of an infon.

Definition 5.29 (Meet of a set of infons, existentialization and negation of infons)   Let $I$ be a set of infons and $i$ be an infon. Then $\bigwedge I$ is called the meet of a set of infons, and $\exists x(i)$ the existentialization of $i$ with respect to $x$. $\neg i$ is called the negation of $i$.

This leads to another axiom.

Axiom 5.38   Let $I$ be a set of infons and $i$ be an infon and $s$ a situation or situoid. Then

• $s \models \bigwedge I$ iff $s \models i$ for all $i \in I$
• $s \models \exists x(i)$ iff for some object $a$, $s\models i'$, where $i'$ is identical to $i$ except for the anchor of $i'$ $anchor(i')=f$ and $f(x)=a$.
• $s \models \neg i$ iff $s \not\models i$.

Using this axiom leaves the ontological status of infons unchanged. They still correspond to pictural states of affairs which correspond to states of affairs. Compound infons do not correspond to pictural states of affairs, but we do not need to introduce such a notion, because we just use compound infons as a convenient way to express more complicated propositions in an easy fashion.