**eJournal: uffmm.org
ISSN 2567-6458, 24.March – 24.March 2021
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de**

##### CONTEXT

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.

##### DERIVATION

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* E_{S} to represent either a given starting state S or to represent as E_{V} a given vision V. Furthermore we have *change rules X* operating on sets of expressions and we can derive sequences of states of expressions <E_{1}, E_{2}, …, E_{n}> by applying the change rules X with the aid of a *simulator Σ* onto these expressions written as

*E _{S} ⊢_{Σ,X }<E_{1}, E_{2}, …, E_{n}>*

Thus given an *initial set of expressions E _{S}* one can derive a whole

*sequence of expression*sets E

_{i}by applying the change rules.

While all individual expressions of the *start set E _{S}* are by assumption classified as

*true*it holds for the derived sets of expressions E

_{i}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 S

_{i}considered as a

*possible future state S*

^{fut}_{i }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 [T_{OKSIMO}]

Thus if we have some human actors A_{hum}, an environment ENV, some starting situation S as part of the environment ENV, a first set of expressions E_{S} 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 T _{oksimo}* as follows:

*T _{OKSIMO}(x) iff x = <ENV, S, A_{hum}, E_{S}, X, Σ, ⊢_{Σ,X}, speak_{L}(), makedecidable()>*

The human actors can describe a given situation S as part of an environment ENV as a set of expressions E_{S} 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 <E

_{1}, E

_{2}, …, E

_{n}> written as

*E _{S} ⊢_{T,Σ,X }<E_{1}, E_{2}, …, E_{n}>*

While the *truth* of the *first set of expressions E _{S}* has been proved in the beginning, the

*truth of the derived sets of expressions*has to be shown explicitly for each set E

_{i}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 [T_{OKSIMO.V}]

One can extend the simple oksimo theory ** T_{OKSIMO}** to a

*biased oksimo theory*if one includes in the theory a set of

**T**_{OKSIMO}_{.V }*vision expressions E*. Vision expressions can describe a

_{V}*possible situation in the future S*which is declared as a goal to be reached. With a given vision document

^{fut}*E*the simulator can check for every new derived set of expressions E

_{V}_{i}to which degree the individual expressions e of the set of

*vision expressions E*

_{V}are already reached.##### FROM THEORY TO ENGINEERING

But one has to keep in mind that the *purely formal achievement* of a given vision document E_{V} does not imply that the corresponding situation S^{fut} is a *real* situation. The corresponding situation S^{fut} 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.*