Remembering

Another phenomenon in everyday life is the fact that we can remember 'past' things. Having some appropriate key which relates at least 'partially' to some past object we can remember objects, whole situations or even some process leading from one situation to another one. Thus remembering $ \rho$ is a kind of mapping taking a concept and producing related material from the past which is 'sufficient similar' to the actual concept $ c_{i}$. Experiments show that the objects remembered $ \{o^{\rho}_{i}\} = \rho(c_{i})$ are usually different from the objects perceived $ \{o^{\pi}_{i}\} = \pi(c_{i})$, $ \rho(c_{i}) \neq \{o^{\pi}_{i}, ...\}$.


$\displaystyle \rho$ $\displaystyle :$ $\displaystyle c_{i} \longmapsto \{o^{\rho}_{i}, ...\}$ (6.24)
$\displaystyle \pi$ $\displaystyle :$ $\displaystyle \emptyset \longmapsto \{o^{\pi}_{i}, ...\}$ (6.25)
$\displaystyle \rho(c_{i})$ $\displaystyle \neq$ $\displaystyle \{o^{\pi}_{i}, ...\}$ (6.26)

Things remembered are again phenomena and therefore it is possible to form abstractions out of these. If one remembers a whole situation $ s \in SIT$ then one remembers a complex object having different kinds of objects connected by relations $ R_{i} \in R$. A process $ PROC$ is based on sets of situations and maps situations into situations.


$\displaystyle PROC(x)$ $\displaystyle iff$ $\displaystyle x = \langle SIT, R, \delta\rangle$ (6.27)
$\displaystyle s$ $\displaystyle \in$ $\displaystyle SIT$ (6.28)
$\displaystyle SIT$ $\displaystyle \subseteq$ $\displaystyle 2^{O}$ (6.29)
$\displaystyle O$ $\displaystyle =$ $\displaystyle \{o_{i}, ...\}$ (6.30)
$\displaystyle R$ $\displaystyle =$ $\displaystyle \{R_{i}, ...\}$ (6.31)
$\displaystyle R_{i}$ $\displaystyle \subseteq$ $\displaystyle O^{n}$ (6.32)
$\displaystyle \delta$ $\displaystyle \subseteq$ $\displaystyle SIT \times SIT$ (6.33)

Usually are the remembered processes $ p \in PROC$ only of a finite length with not too many details.

Gerd Doeben-Henisch 2012-03-31