Discussion of Barwisean situation theory

Let us review some of the decisions made by Barwise in his development of situation theory.

First we note, that there is some kind of appropriateness between relations and the arguments of those relations, that make up infons. Barwise did not give a formal definition of what is meant by appropriateness. Intuitively, while formalizing knowledge about a given situation, a human designer has an understanding of what is meant by it. However, an intelligent agent in general does not see the difference between $\models \langle\langle eat, Alice, meat; 1\rangle\rangle$ and $\models \langle\langle eat, Alice, 23;1\rangle\rangle$ without further knowledge. What certainly is needed is some kind of representation of what categories of objects exist in our world, and what categories a certain relation can take as its arguments. Understandingly, this goes far beyond the scope of situation theory, and we will discuss this in chapter 4.

Also, it is not enough that $\langle\langle eat, Alice,23; 0\rangle\rangle$ should hold, but that $\langle\langle eat,Alice,23\rangle\rangle$ can never be true, it should not be considered an infon at all. A state of affair or infon of this kind should be considered nonsensical (in the spirit of Wittgenstein).

On the other hand, if we consider an algebra of infons permitting conjunction or disjunction of it, we have to decide whether we want to consider infons of the kind $\langle\langle R,x_1,...,x_n;1\rangle\rangle \land\langle\langle R,x_1,...,x_n;0\rangle\rangle$ infons. Our intuition behind calling infons infons was that they capture information. Infons of this kind, contradictions or tautologies, do not contain any information at all. Of course they are false (or true) in every situation, but they are not about situations at all. We do not want to consider these as infons either. Infons, in our approach, contain information about situations or the world, they are meaningful. There must be a possible situation for any infon to hold, and another possible situation for an infon to not hold. Otherwise we will not consider them infons at all.

Barwise refers to spatio-temporal entities in his approach, but never clarifies what he means by it. It is not obvious whether he understands situations as having a duration no matter how short, or if he allows them to exist only at an instant, a point in time, or both. He states that they exist in time and space, therefore they occupy space, but whether the space (or the time) have to be connected, is unclear. After all, even the most basic structure of space and time is unclear. Is time and space unlimited? Are they dense? Or linear?

Perhaps he did not want to commit himself to such fundamental decisions, and leave it for further work, or for any applicant of situation theory to decide. However, we argue that the structure of situations cannot be understood without a theory of time and space. One way to complete situation theory with a theory of space and time is to use some existing theory of it and add its axioms to the ones of situation theory, and state an appropriate relation between both, situation theory and the preferred theory of time and space. This appears to be promising, because one could alter the axioms of time and space and compare their expressive powers.

We will argue later, that there is an ontological difference between situations that have a durations and those, that exist at a point in time. Therefore, we will consider only one theory of time and space, the theory used in the GOL ontology, sometimes called glass model.

Probably the most difficult task in amending situation theory is to define some conditions for a situation to be called ``situation''. Barwise refers to some closure conditions occasionally, but never states one of them.

Let us consider an example. John is kissing Mary, while laying on a bank in a park. This situation is taking place at a certain time $t$, and a certain place $s$. We certainly want to consider this a situation. Let us imagine now the same situation, but with the bank gone. Both of them are still laying, but the bank is outside our situation. So it seems as if they were floating in the air, about 75 cm above the ground. One might argue that this is impossible, and therefore should not be considered a situation at all. On the other hand, it is a part of reality, and maybe we only need to consider the information that John is kissing Mary while laying, at a certain spatio-temporal location, and they are about 50 centimeter above the ground. If we know about gravity and the mass of John and Mary, we could argue that there has to be some force keeping them above the ground, but do not know what this force is.

Also, more abstract, we could ask if a set can be viewed as a situation. The elements of a set may stand to each other in certain relations, and the set is some whole entity. What if the set is infinite? Or undecidable?

So we could try to find some kind of closure conditions situations have to fulfill. We will attempt this later when we introduce our ontology based situation theory.