Infons

Infons are necessarily existing, abstract entities. They contain information about states of affairs, and therefore about how the world is. They are used to communicate knowledge about states of affairs. They are pictures of states of affairs plus information about its existence, and therefore pictures of parts of reality. They are the entities that exist in an agents mind, when she perceives a state of affairs and assigns it to some part of reality.

Infons are about states of affairs. They are close to set-theoretical constructions, and therefore to a certain degree extensional, as they are founded upon a pictural state of affairs, which is a part of reality, and a function, which is a set-theoretical construct.

A basic infon consists of a relation $R$, a number of objects, $a_1,...,a_n$ and a polarity $p$, where $p \in \{0,1\}$. We will denote basic infons as $\langle\langle R,a_1,...,a_n;p\rangle\rangle$.

Until now, they look quite similar to states of affairs, and in order to avoid confusion about whether we just introduced infons because we did not want to commit ourselves to non-obtaining states of affairs, we will say some things about their ontological relationship to states of affairs.

Infons carry information about states of affairs in the world. They are supposed to describe the states of affairs that are the case in the world or a part of it. The knowledge or information about the absence of a state of affairs is the kind of information carried by a negative basic infon.

A positive infon does not say more about states of affairs in some part of the world than a negative infon. Infons are chunks of information about models of parts of the world in an agent's mind. If in such a model the agent asserts a positive infon, she believes the corresponding state of affairs to exist in the part of the world she constructed a model for. If she asserts a negative infon, she believes the corresponding state of affairs not to exist in this part of the world.

What does it mean, that a state of affairs ``corresponds'' to an infon? We could just say, that an infon $\phi=\langle\langle R,a_1,...,a_n;p\rangle\rangle$ and a state of affairs $s=\langle\langle P,b_1,...,b_n \rangle\rangle$ correspond, if $R=P$ and for $i=1..n$: $a_i=b_i$. But could we justify this? We said that states of affairs exist in the world, in a configuration of objects, while infons exist in an agents mind, as a model for some part of the world. Therefore it would be highly implausible, if we said that $R$ is identical to $P$ and all the objects of the real world are identical to objects in the agents mind. While $R$ and $P$ may be identical, as we will see later, $a_1,...,a_n$ and $b_1,...,b_n$ are certainly not.

The start of the solution to the question of correspondence between states of affairs and infons can be found in tractatus. Wittgenstein distinguishes between states of affairs and pictures of states of affairs. He wrote:

We make to ourselves pictures of facts.

The picture presents the facts in logical space, the existence and non-existence of atomic facts.

The picture is a model of reality.

To the objects correspond in the picture the elements of the picture.

The elements of the picture stand, in the picture, for the objects.

The picture consists in the fact that its elements are combined with one another in a definite way.

This may answer our question. There are entities in pictures of states of affairs, entities corresponding to objects. Those are the elements of the picture. We could, therefore, say, that the objects in infons correspond to real objects. The problem is again with negative infons. Consider the infon $\langle\langle Sees, Kay, unicorn; 0 \rangle\rangle$. Then there are two possibilities, that could account for this infons not obtaining. Kay and the unicorn exist, but they just do not happen to stand in the relation $Sees$. Or Kay or the unicorn do not exist, and therefore they cannot stand in this relation. It just so happens that unicorns are not part of our world, and the term ``unicorn'' does not stand for an object in our world.

We could turn for infons to ``soft actualism'', and state that all entities that occur in a picture of a state of affairs do exist in the world. But we are not willing to do this, as it would limit us too far in our further discussion about situoids and worlds. We will instead follow another path, again laid out by Wittgenstein in tractatus:

That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.

This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.

The form of representation is the possibility that the things are combined with one another as are the elements of the picture.

We will say, that infons are about possibilities of how things could be or not be. We will say, that an infon $\phi$ corresponds to a state of affairs $s$, if there is a possible world $w$, such that $s$ is a fact of $w$, and $\phi$ has the same structure (the same characteristic relation) as $s$ and the objects of $s$ correspond to the elements of $\phi$. Before we investigate correspondence of the relations and objects to the elements of the picture of the state of affairs, we state, that for every infon, positive or negative, there has to exist a state of affairs which is a fact in some (possible) world, and the infon ``corresponds'' to this state of affairs. A negative infon therefore contains the information, that the state of affairs is not present in the part of reality in concern. However, an infon has to be possible in the sense, that there has to exist a world, in which the infon corresponds to a state of affairs.

Now again back to infons and objects. We said that the objects correspond to the elements of the infon. This suggests, that there is a function, or a functional relation, between objects and the entities present in infons. The elements of the picture are abstract entities, representing objects. For the last time now, let us see, what Wittgenstein has to say about this relation:

According to this view the representing relation which makes it a picture, also belongs to the picture.

The representing relation consists of the co-ordinations of the elements of the picture and the things.

Therefore we state, that there is an assignment function $a$, assigning objects to picture elements, elements of the infon, and therefore filling the arguments of the constituting relation $R$ of the infon. The assignment function is a part of the infon. The assignment function does not necessarily have to assign an object to every possible argument of the relation $R$ (it may be a partial function). The same function has been used by Barwise in barsit in situation theory as ``assignment'' for, what he called, states of affairs.

The elements of the picture, the parameters, are related to one another as the objects in the state of affairs are related to one another. States of affairs consist of a relator and its arguments are filled by objects. Pictures of states of affairs consist of a relator, and its arguments are filled by picture elements, parameters, and the assignment function $a$.

The picture consists of its elements being in relation to one another in a determinate way. Therefore, pictures of states of affairs are special states of affairs.

Something has to be identical, for the picture to be a picture of a state of affairs. Wittgenstein called this the form of the picture: The possibility, that things are related to one another as are the elements of the picture. Therefore, for a picture to be a picture, the following condition has to be met: ``The elements of the picture must be related to one another as the elements of reality could be related to one another. This means: pictorial representation is possible at all only if the possibilities of combination of the elements of the picture are the same as the possibilities of combination of the elements of reality.''morris This will become clearer in the next section.

Definition 5.1 (pictural state of affairs)   A picture of a states of affairs or pictural state of affairs is a state of affairs. It consists of a relation $R$ with a set of arguments $Arg(R)$ and an assignment function $a: Arg(R)\mapsto Entity$. The pictural state of affairs is called complete, if $a$ assigns every $arg\in Arg(R)$ an object, otherwise it is called incomplete. Pictural states of affairs are noted $\langle\langle R,a\rangle\rangle$, or $\langle\langle R,a_1,...,a_n \rangle\rangle$ if it is clear from the context, that a pictural state of affairs is denoted and that $a_1,...,a_n$ are assignments. The class of all pictural states of affairs is called $picSOA$.

The infon, as a piece of information in an agent's mind, describes the presence or absence of a state of affairs. Because infons exist in mind, pictures of states of affairs have to be used, to refer to the state of affairs. An infon consists of a function $f:picSOA \mapsto \{0,1\}$ and the picture of a state of affairs.

Definition 5.2 (Infon)   An infon consists of a pictural state of affairs $\phi$ and a function $f:picSOA \mapsto \{0,1\}$. Let $\phi=\langle\langle R,a \rangle\rangle$ be a pictural state of affairs. Then we note an appropriate infon $\langle\langle R,a;p \rangle\rangle$, where $p \in \{0,1\}$.

To obtain a complete description of infons and their relation to pictures of states of affairs and states of affairs, we have to formalize the correspondence relation.