ISSN 2567-6458, 24.March – 24.March 2021
Author: Gerd Doeben-Henisch
This text is part of a philosophy of science analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive posts dedicated to the HMI-Analysis for this software.
In formal logic exists the concept of logical derivation ‘⊢’ written as
E ⊢X e
saying that one can get the expression e out of the set of expressions E by applying the rules X.
In the oksimo case we have sets of expressions ES to represent either a given starting state S or to represent as EV a given vision V. Furthermore we have change rules X operating on sets of expressions and we can derive sequences of states of expressions <E1, E2, …, En> by applying the change rules X with the aid of a simulator Σ onto these expressions written as
ES ⊢Σ,X <E1, E2, …, En>
Thus given an initial set of expressions ES one can derive a whole sequence of expression sets Ei by applying the change rules.
While all individual expressions of the start set ES are by assumption classified as true it holds for the derived sets of expressions Ei that these expressions are correct with regard to the used change rules X but whether these sets of expressions are also true with regard to a given situation Si considered as a possible future state Sfuti has to be proved separately! The reason for this unclear status results from the fact that the change rules X represent changes which the authoring experts consider as possible changes which they want to apply but they cannot guarantee the empirical validity for all upcoming times only by thinking. This implicit uncertainty can be handled a little bit with the probability factor π of an individual change rule. The different degrees of certainty in the application of a change rule can give an approximation of this uncertainty. Thus as longer the chain of derivations is becoming as lower the assumed probability will develop.
SIMPLE OKSIMO THEORY [TOKSIMO]
Thus if we have some human actors Ahum, an environment ENV, some starting situation S as part of the environment ENV, a first set of expressions ES representing only true expressions with regard to the starting situation S, a set of elaborated change rules X, and a simulator Σ then one can define a simple oksimo-like theory Toksimo as follows:
TOKSIMO(x) iff x = <ENV, S, Ahum, ES, X, Σ, ⊢Σ,X, speakL(), makedecidable()>
The human actors can describe a given situation S as part of an environment ENV as a set of expressions ES which can be proved with makedecidable() as true. By defining a set of change rules X and a simulator Σ one can define a formal derivation relation ⊢Σ,X which allows the derivation of a sequence of sets of expressions <E1, E2, …, En> written as
ES ⊢T,Σ,X <E1, E2, …, En>
While the truth of the first set of expressions ES has been proved in the beginning, the truth of the derived sets of expressions has to be shown explicitly for each set Ei separately. Given is only the formal correctness of the derived expressions according to the change rules X and the working of the simulator.
VALIDADED SIMPLE OKSIMO THEORY [TOKSIMO.V]
One can extend the simple oksimo theory TOKSIMO to a biased oksimo theory TOKSIMO.V if one includes in the theory a set of vision expressions EV. Vision expressions can describe a possible situation in the future Sfut which is declared as a goal to be reached. With a given vision document EV the simulator can check for every new derived set of expressions Ei to which degree the individual expressions e of the set of vision expressions EV are already reached.
FROM THEORY TO ENGINEERING
But one has to keep in mind that the purely formal achievement of a given vision document EV does not imply that the corresponding situation Sfut is a real situation. The corresponding situation Sfut is first of all only an idea in the mind of the experts. To transfer this idea into the real environment as a real situation is a process on its own known as engineering.