Infons

Let us now consider information. Information is built up from basic information units, states of affairs or infon.

Definition 3.1 (Infon, Polarity, Major Constituent, Minor Constituent)   A relation $R$ and an appropriate assignment $a$ of objects determine two basic infons. The notion of these infons is $\langle\langle R,a;1\rangle\rangle$ and $\langle\langle R,a;0\rangle\rangle$ or, in case the arguments have been ordered, $\langle\langle R,a_1,...,a_n;1\rangle\rangle$ and $\langle\langle R,a_1,...,a_n;0\rangle\rangle$. Let $\phi = \langle\langle R,a;i\rangle\rangle$, then $R$ is called major constituent of $\phi$, each $a_{arg} \in Arg(R)$ is called a minor constituent of $\phi$ and the value $i \in \{0,1\}$ is called the polarity of $\phi$. Basic infons with polarity $1$ are called positive, with polarity 0 negative.

A basic infon that obtains is called a fact. Given a relation $R$ and an appropriate assignment $a$, at most one of the defined basic infons obtains. We write $\models \phi$ for a basic infon that obtains.