Changes

Two situations are said to coincide, if the time-boundaries at which they exist coincide. Two situoids are called ``successive situoids'' if the terminal situation of the first coincided with the initial situation of the second.

Now let us define what we mean by a change.

Definition 5.27 (Change)   A change $c$ is an ordered pair of situations, $s_1$ and $s_2$, such that $S(s_1)\not= S(s_2)$ and $tbs(s_1)<tbs(s_2)$. We will note a change of this kind as $c=(s_1,s_2)$. The class of all changes is called $Change$.

There are two kinds of changes, instantaneous changes and eventual changes.

The first type appears for example, when we consider a lamp that is being turned on as a situoid. In the initial situation, the lamp is off. Then there is the process of turning the lamp on. Let us end this situoid and the process of turning on the lamp with the lamp still being off. This is the terminal situation of the first situoid. A successive situoid starts with the lamp being on. The initial situation of the second, $s_2$, coincides with the terminal situation of the first, $s_1$. At least one infon changed polarity, and therefore $S(s_1)\not= S(s_2)$, and $(s_1,s_2)$ is a change.

Let us consider the same process of turning on a lamp in a somewhat larger situoid. Then, the lamp is turned off in the initial situation, $s_1$, but turned on in the terminal situation, $s_2$. Those two situations do not exist on coinciding time boundaries, but again, at least one infon changed polarity, and therefore $(s_1,s_2)$ is again a change.

Considering two situations, $s_1$ and $s_2$. What happens, if there is an infon $\phi$ that obtains in $s_1$, but neither $\phi$ nor its complement obtains in $s_2$. Would we consider this a change? Our answer is yes, because somehow, information appears to have got lost. If we start out knowing the lamp is turned off, but we end up with a situation in which no information about the lamp's being on or off is present, certainly something changed.

Another problem appears, when we consider two seemingly unrelated situations, for example one, $s_1$, with the lamp being turned off, and another one, $s_2$, with John kissing Mary. Most people would not consider this a proper change, although both situations are totally different. This may even be the case with coinciding situations. As changes happen in the frame of situoids, we will state another axiom, in order to prevent these types of changes.

Axiom 5.37  

$$\forall c (Change(c)\land c=(s_1,s_2) \rightarrow \exists s (Situoid(s) \land s_1 \leq _{sit} s \land s_2 \leq _{sit} s))$$

Changes therefore have to be considered with respect to a situoid.