AAI THEORY V2 – DEFINING THE CONTEXT

eJournal: uffmm.org,
ISSN 2567-6458, 24.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the second chapter where you have to define the context of the problem, which should be analyzed.

DEFINING THE CONTEXT OF PROBLEM P

  1. A defined problem P identifies at least one property associated with  a configuration which has a lower level x than a value y inferred by an accepted standard E.
  2. The property P is always part of some environment ENV which interacts with the problem P.
  3. To approach an improved configuration S measured by  some standard E starting with a  problem P one  needs a process characterized by a set of necessary states Q which are connected by necessary changes X.
  4. Such a process can be described by an actor story AS.
  5. All properties which belong to the whole actor story and therefore have to be satisfied by every state q of the actor story  are called  non-functional process requirements (NFPRs). If required properties are are associate with only one state but for the whole state, then these requirements are called non-functional state requirements (NFSRs).
  6. An actor story can include many different sequences, where every sequence is called a path PTH.  A finite set of paths can represent a task T which has to be fulfilled. Within the environment of the defined problem P it mus be possible to identify at least one task T to be realized from some start state to some goal state. The realization of a task T is assumed to be ‘driven’ by input-output-systems which are called actors A.
  7. Additionally it mus be possible to identify at least one executing actor A_exec doing a  task and at least one actor assisting A_ass the executing actor to fulfill the task.
  8. A state q represents all needed actors as part of the associated environment ENV. Therefore a  state q can be analyzed as a network of elements interacting with each other. But this is only one possible structure for an analysis besides others.
  9. For the   analysis of a possible solution one can distinguish at least two overall strategies:
    1. Top-down: There exists a group of experts EXPs which will analyze a possible solution, will test these, and then will propose these as a solution for others.
    2. Bottom-up: There exists a group of experts EXPs too but additionally there exists a group of customers CTMs which will be guided by the experts to use their own experience to find a possible solution.

EXAMPLE

The mayor of a city has identified as a  problem the relationship between the actual population number POP,    the amount of actual available  living space LSP0, and the  amount of recommended living space LSPr by some standard E.  The population of his city is steadily interacting with populations in the environment: citizens are moving into the environment MIGR- and citizens from the environment are arriving MIGR+. The population,  the city as well as the environment can be characterized by a set of parameters <P1, …, Pn> called a configuration which represents a certain state q at a certain point of time t. To convert the actual configuration called a start state q0 to a new configuration S called a goal state q+ with better values requires the application of a defined set of changes Xs which change the start state q0 stepwise into a sequence of states qi which finally will end up in the desired goal state q+. A description of all these states necessary for the conversion of the start state q0 into the goal state q+ is called here an actor story AS. Because a democratic elected  mayor of the city wants to be ‘liked’ by his citizens he will require that this conversion process should end up in a goal state which is ‘not harmful’ for his citizens, which should support a ‘secure’ and ‘safety’ environment, ‘good transportation’ and things like that. This illustrates non-functional state requirements (NFSRs). Because the mayor wants also not to much trouble during the conversion process he will also require some limits for the whole conversion process, this is for the whole actor story. This illustrates non-functional process requirements (NFPRs). To realize the intended conversion process the mayor needs several executing actors which are doing the job and several other assistive actors helping the executing actors. To be able to use the available time and resources ‘effectively’ the executing actors need defined tasks which have to be realized to come from one state to the next. Often there are more than one sequences of states possible either alternatively or in parallel. A certain state at a certain point of time t can be viewed as a network where all participating actors are in many ways connected with each other, interacting in several ways and thereby influencing each other. This realizes different kinds of communications with different kinds of contents and allows the exchange of material and can imply the change of the environment. Until today the mayors of cities use as their preferred strategy to realize conversion processes selected small teams of experts doing their job in a top-down manner leaving the citizens more or less untouched, at least without a serious participation in the whole process. From now on it is possible and desirable to twist the strategy from top-down to bottom up. This implies that the selected experts enable a broad communication with potentially all citizens which are touched by a conversion and including  the knowledge, experience, skills, visions etc. of these citizens  by applying new methods possible in the new digital age.

 

 

BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. The Limits of Classic Probability

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

Last Corrections: 30.Dec.2018

CONTEXT

This is a continuation from the post about QL Basics Concepts Part 1. The general topic here is the analysis of properties of human behavior, actually narrowed down to the statistical properties. From the different possible theories applicable to statistical properties of behavior here the one called CPT (classical probability theory) is selected for a short examination.

SUMMARY

An analysis of the classical probability theory shows that the empirical application of this theory is limited to static sets of events and probabilities. In the case of biological systems which are adaptive with regard to structure and cognition this does not work. This yields the question whether a quantum probability theory approach does work or not.

THE CPT IDEA

  1. Before we are looking  to the case of quantum probability theory (QLPT) let us examine the case of a classical probability theory (CPT) a little bit more.
  2. Generally one has to distinguish the symbolic formal representation of a theory T and some domain of application D distinct from the symbolic representation.
  3. In principle the domain of application D can be nearly anything, very often again another symbolic representation. But in the case of empirical applications we assume usually some subset of ’empirical events’ E of the ’empirical (real) world’ W.
  4. For the following let us assume (for a while) that this is the case, that D is a subset of the empirical world W.
  5. Talking about ‘events in an empirical real world’ presupposes that there there exists a ‘procedure of measurement‘ using a ‘previously defined standard object‘ and a ‘symbolic representation of the measurement results‘.
  6. Furthermore one has to assume a community of ‘observers‘ which have minimal capabilities to ‘observe’, which implies ‘distinctions between different results’, some ‘ordering of successions (before – after)’, to ‘attach symbols according to some rules’ to measurement results, to ‘translate measurement results’ into more abstract concepts and relations.
  7. Thus to speak about empirical results assumes a set of symbolic representations of those events as a finite set of symbolic representations which represent a ‘state in the real world’ which can have a ‘predecessor state before’ and – possibly — a ‘successor state after’ the ‘actual’ state. The ‘quality’ of these measurement representations depends from the quality of the measurement procedure as well as from the quality of the cognitive capabilities of the participating observers.
  8. In the classical probability theory T_cpt as described by Kolmogorov (1932) it is assumed that there is a set E of ‘elementary events’. The set E is assumed to be ‘complete’ with regard to all possible events. The probability P is coming into play with a mapping from E into the set of positive real numbers R+ written as P: E —> R+ or P(E) = 1 with the assumption that all the individual elements e_i of E have an individual probability P(e_i) which obey the rule P(e_1) + P(e_2) + … + P(e_n) = 1.
  9. In the formal theory T_cpt it is not explained ‘how’ the probabilities are realized in the concrete case. In the ‘real world’ we have to identify some ‘generators of events’ G, otherwise we do not know whether an event e belongs to a ‘set of probability events’.
  10. Kolmogorov (1932) speaks about a necessary generator as a ‘set of conditions’ which ‘allows of any number of repetitions’, and ‘a set of events can take place as a result of the establishment of the condition’. (cf. p.3) And he mentions explicitly the case that different variants of the a priori assumed possible events can take place as a set A. And then he speaks of this set A also of an event which has taken place! (cf. p.4)
  11. If one looks to the case of the ‘set A’ then one has to clarify that this ‘set A’ is not an ordinary set of set theory, because in a set every member occurs only once. Instead ‘A’ represents a ‘sequence of events out of the basic set E’. A sequence is in set theory an ‘ordered set’, where some set (e.g. E) is mapped into an initial segment  of the natural numbers Nat and in this case  the set A contains ‘pairs from E x Nat|\n’  with a restriction of the set Nat to some n. The ‘range’ of the set A has then ‘distinguished elements’ whereby the ‘domain’ can have ‘same elements’. Kolmogorov addresses this problem with the remark, that the set A can be ‘defined in any way’. (cf. p.4) Thus to assume the set A as a set of pairs from the Cartesian product E x Nat|\n with the natural numbers taken from the initial segment of the natural numbers is compatible with the remark of Kolmogorov and the empirical situation.
  12. For a possible observer it follows that he must be able to distinguish different states <s1, s2, …, sm> following each other in the real world, and in every state there is an event e_i from the set of a priori possible events E. The observer can ‘count’ the occurrences of a certain event e_i and thus will get after n repetitions for every event e_i a number of occurrences m_i with m_i/n giving the measured empirical probability of the event e_i.
  13. Example 1: Tossing a coin with ‘head (H)’ or ‘tail (T)’ we have theoretically the probabilities ‘1/2’ for each event. A possible outcome could be (with ‘H’ := 0, ‘T’ := 1): <((0,1), (0,2), (0,3), (1,4), (0,5)> . Thus we have m_H = 4, m_T = 1, giving us m_H/n = 4/5 and m_T/n = 1/5. The sum yields m_H/n + m_T/n = 1, but as one can see the individual empirical probabilities are not in accordance with the theory requiring 1/2 for each. Kolmogorov remarks in his text  that if the number of repetitions n is large enough then will the values of the empirically measured probability approach the theoretically defined values. In a simple experiment with a random number generator simulating the tossing of the coin I got the numbers m_Head = 4978, m_Tail = 5022, which gives the empirical probabilities m_Head/1000 = 0.4977 and m_Teil/ 1000 = 0.5021.
  14. This example demonstrates while the theoretical term ‘probability’ is a simple number, the empirical counterpart of the theoretical term is either a simple occurrence of a certain event without any meaning as such or an empirically observed sequence of events which can reveal by counting and division a property which can be used as empirical probability of this event generated by a ‘set of conditions’ which allow the observed number of repetitions. Thus we have (i) a ‘generator‘ enabling the events out of E, we have (ii) a ‘measurement‘ giving us a measurement result as part of an observation, (iii) the symbolic encoding of the measurement result, (iv) the ‘counting‘ of the symbolic encoding as ‘occurrence‘ and (v) the counting of the overall repetitions, and (vi) a ‘mathematical division operation‘ to get the empirical probability.
  15. Example 1 demonstrates the case of having one generator (‘tossing a coin’). We know from other examples where people using two or more coins ‘at the same time’! In this case the set of a priori possible events E is occurring ‘n-times in parallel’: E x … x E = E^n. While for every coin only one of the many possible basic events can occur in one state, there can be n-many such events in parallel, giving an assembly of n-many events each out of E. If we keeping the values of E = {‘H’, ‘T’} then we have four different basic configurations each with probability 1/4. If we define more ‘abstract’ events like ‘both the same’ (like ‘0,0’, ‘1,1’) or ‘both different’ (like ‘0,1’. ‘1,0’), then we have new types of complex events with different probabilities, each 1/2. Thus the case of n-many generators in parallel allows new types of complex events.
  16. Following this line of thinking one could consider cases like (E^n)^n or even with repeated applications of the Cartesian product operation. Thus, in the case of (E^n)^n, one can think of different gamblers each having n-many dices in a cup and tossing these n-many dices simultaneously.
  17. Thus we have something like the following structure for an empirical theory of classical probability: CPT(T) iff T=<G,E,X,n,S,P*>, with ‘G’ as the set of generators producing out of E events according to the layout of the set X in a static (deterministic) manner. Here the  set E is the set of basic events. The set X is a ‘typified set’ constructed out of the set E with t-many applications of the Cartesian operation starting with E, then E^n1, then (E^n1)^n2, …. . ‘n’ denotes the number of repetitions, which determines the length of a sequence ‘S’. ‘P*’ represents the ’empirical probability’ which approaches the theoretical probability P while n is becoming ‘big’. P* is realized as a tuple of tuples according to the layout of the set X  where each element in the range of a tuple  represents the ‘number of occurrences’ of a certain event out of X.
  18. Example: If there is a set E = {0,1} with the layout X=(E^2)^2 then we have two groups with two generators each: <<G1, G2>,<G3,G4>>. Every generator G_i produces events out of E. In one state i this could look like  <<0, 0>,<1,0>>. As part of a sequence S this would look like S = <….,(<<0, 0>,<1,0>>,i), … > telling that in the i-th state of S there is an occurrence of events like shown. The empirical probability function P* has a corresponding layout P* = <<m1, m2>,<m3,m4>> with the m_j as ‘counter’ which are counting the occurrences of the different types of events as m_j =<c_e1, …, c_er>. In the example there are two different types of events occurring {0,1} which requires two counters c_0 and c_1, thus we would have m_j =<c_0, c_1>, which would induce for this example the global counter structure:  P* = <<<c_0, c_1>, <c_0, c_1>>,<<c_0,  c_1>,<c_0, c_1>>>. If the generators are all the same then the set of basic events E is the same and in theory   the theoretical probability function P: E —> R+ would induce the same global values for all generators. But in the empirical case, if the theoretical probability function P is not known, then one has to count and below the ‘magic big n’ the values of the counter of the empirical probability function can be different.
  19. This format of the empirical classical  probability theory CPT can handle the case of ‘different generators‘ which produce events out of the same basic set E but with different probabilities, which can be counted by the empirical probability function P*. A prominent case of different probabilities with the same set of events is the case of manipulations of generators (a coin, a dice, a roulette wheel, …) to deceive other people.
  20. In the examples mentioned so far the probabilities of the basic events as well as the complex events can be different in different generators, but are nevertheless  ‘static’, not changing. Looking to generators like ‘tossing a coin’, ‘tossing a dice’ this seams to be sound. But what if we look to other types of generators like ‘biological systems’ which have to ‘decide’ which possible options of acting they ‘choose’? If the set of possible actions A is static, then the probability of selecting one action a out of A will usually depend from some ‘inner states’ IS of the biological system. These inner states IS need at least the following two components:(i) an internal ‘representation of the possible actions’ IS_A as well (ii) a finite set of ‘preferences’ IS_Pref. Depending from the preferences the biological system will select an action IS_a out of IS_A and then it can generate an action a out of A.
  21. If biological systems as generators have a ‘static’ (‘deterministic’) set of preferences IS_Pref, then they will act like fixed generators for ‘tossing a coin’, ‘tossing a dice’. In this case nothing will change.  But, as we know from the empirical world, biological systems are in general ‘adaptive’ systems which enables two kinds of adaptation: (i) ‘structural‘ adaptation like in biological evolution and (ii) ‘cognitive‘ adaptation as with higher organisms having a neural system with a brain. In these systems (example: homo sapiens) the set of preferences IS_Pref can change in time as well as the internal ‘representation of the possible actions’ IS_A. These changes cause a shift in the probabilities of the events manifested in the realized actions!
  22. If we allow possible changes in the terms ‘G’ and ‘E’ to ‘G+’ and ‘E+’ then we have no longer a ‘classical’ probability theory CPT. This new type of probability theory we can call ‘non-classic’ probability theory NCPT. A short notation could be: NCPT(T) iff T=<G+,E+,X,n,S,P*> where ‘G+’ represents an adaptive biological system with changing representations for possible Actions A* as well as changing preferences IS_Pref+. The interesting question is, whether a quantum logic approach QLPT is a possible realization of such a non-classical probability theory. While it is known that the QLPT works for physical matters, it is an open question whether it works for biological systems too.
  23. REMARK: switching from static generators to adaptive generators induces the need for the inclusion of the environment of the adaptive generators. ‘Adaptation’ is generally a capacity to deal better with non-static environments.

See continuation here.

AASE – Actor-Actor Systems Engineering. Theory & Applications. Micro-Edition (Vers.9)

eJournal: uffmm.org, ISSN 2567-6458
13.June  2018
Email: info@uffmm.org
Authors: Gerd Doeben-Henisch, Zeynep Tuncer,  Louwrence Erasmus
Email: doeben@fb2.fra-uas.de
Email: gerd@doeben-henisch.de

PDF

CONTENTS

1 History: From HCI to AAI …
2 Different Views …
3 Philosophy of the AAI-Expert …
4 Problem (Document) …
5 Check for Analysis …
6 AAI-Analysis …
6.1 Actor Story (AS) . . . . . . . . . . . . . . . . . . . . . . . . .
6.1.1 Textual Actor Story (TAS) . . . . . . . . . . . . . . .
6.1.2 Pictorial Actor Story (PAT) . . . . . . . . . . . . . .
6.1.3 Mathematical Actor Story (MAS) . . . . . . . . . . .
6.1.4 Simulated Actor Story (SAS) . . . . . . . . . . . . .
6.1.5 Task Induced Actor Requirements (TAR) . . . . . . .
6.1.6 Actor Induced Actor Requirements (UAR) . . . . . .
6.1.7 Interface-Requirements and Interface-Design . . . .
6.2 Actor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.2.1 Actor and Actor Story . . . . . . . . . . . . . . . . .
6.2.2 Actor Model . . . . . . . . . . . . . . . . . . . . . .
6.2.3 Actor as Input-Output System . . . . . . . . . . . .
6.2.4 Learning Input-Output Systems . . . . . . . . . . . .
6.2.5 General AM . . . . . . . . . . . . . . . . . . . . . .
6.2.6 Sound Functions . . . . . . . . . . . . . . . . . . .
6.2.7 Special AM . . . . . . . . . . . . . . . . . . . . . .
6.2.8 Hypothetical Model of a User – The GOMS Paradigm
6.2.9 Example: An Electronically Locked Door . . . . . . .
6.2.10 A GOMS Model Example . . . . . . . . . . . . . . .
6.2.11 Further Extensions . . . . . . . . . . . . . . . . . .
6.2.12 Design Principles; Interface Design . . . . . . . . .
6.3 Simulation of Actor Models (AMs) within an Actor Story (AS) .
6.4 Assistive Actor-Demonstrator . . . . . . . . . . . . . . . . . .
6.5 Approaching an Optimum Result . . . . .
7 What Comes Next: The Real System
7.1 Logical Design, Implementation, Validation . . . .
7.2 Conceptual Gap In Systems Engineering? . . .
8 The AASE-Paradigm …
References

Abstract

This text is based on the the paper “AAI – Actor-Actor Interaction. A Philosophy of Science View” from 3.Oct.2017 and version 11 of the paper “AAI – Actor-Actor Interaction. An Example Template” and it   transforms these views in the new paradigm ‘Actor- Actor Systems Engineering’ understood as a theory as well as a paradigm for and infinite set of applications. In analogy to the slogan ’Object-Oriented Software Engineering (OO SWE)’ one can understand the new acronym AASE as a systems engineering approach where the actor-actor interactions are the base concepts for the whole engineering process. Furthermore it is a clear intention to view the topic AASE explicitly from the point of view of a theory (as understood in Philosophy of Science) as well as from the point of view of possible applications (as understood in systems engineering). Thus the classical term of Human-Machine Interaction (HMI) or even the older Human-Computer Interaction (HCI) is now embedded within the new AASE approach. The same holds for the fuzzy discipline of Artificial Intelligence (AI) or the subset of AI called Machine Learning (ML). Although the AASE-approach is completely in its beginning one can already see how powerful this new conceptual framework  is.

 

 

ACTOR-ACTOR INTERACTION. Philosophy of the Actor

eJournal: uffmm.org, ISSN 2567-6458
16.March 2018
Email: info@uffmm.org
Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de
Frankfurt University of Applied Sciences (FRA-UAS)
Institut for New Media (INM, Frankfurt)

PDF

CONTENTS

I   A Vision as a Problem to be Solved … 1
II   Language, Meaning & Ontology …  2
     II-A   Language Levels . . . . . . . . .  . . 2
     II-B  Common Empirical Matter .  . . . . . 2
     II-C   Perceptual Levels . . . . . . .  . . . . 3
     II-D   Space & Time . . . . . . . .  . . . . . 4
     II-E    Different Language Modes . . . 4
     II-F    Meaning of Expressions & Ontology … 4
     II-G   True Expressions . . . . . . .  . . . .  5
     II-H   The Congruence of Meaning  . . . .  5
III   Actor Algebra … 6
IV   World Algebra  … 7
V    How to continue … 8
VI References … 8

Abstract

As preparation for this text one should read the chapter about the basic layout of an Actor-Actor Analysis (AAA) as part of an systems engineering process (SEP). In this text it will be described which internal conditions one has to assume for an actor who uses a language to talk about his observations oft he world to someone else in a verifiable way. Topics which are explained in this text are e.g. ’language’,’meaning’, ’ontology’, ’consciousness’, ’true utterance’, ’synonymous expression.

AAI – Actor-Actor Interaction. A Toy-Example, No.1

eJournal: uffmm.org, ISSN 2567-6458
13.Dec.2017
Email: info@uffmm.org

Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Contents

1 Problem ….. 3
2 AAI-Check ….. 3
3 Actor-Story (AS) …..  3
3.1 AS as a Text . . . . . . . . . . . . . . . . . .3
3.2 Translation of a Textual AS into a Formal AS …… 4
3.3 AS as a Formal Expression . . . . . . . . . .4
3.4 Translation of a Formal AS into a Pictorial AS… 5
4 Actor-Model (AM) …..  5
4.1 AM for the User as a Text . . . . . . . . . . . . . . . . . . . . . . . . . .  . . . .6
4.2 AM for the System as a Text . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Combined AS and AM as a Text …..  6
5.1 AM as an Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
6 Simulation …..  7
6.1 Simulating the AS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
6.2 Simulating the AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
6.3 Simulating AS with AM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7 Appendix: Formalisms ….. 8
7.1 Set of Strings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9
7.2 Predicate Language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
8 Appendix: The Meaning of Expressions …11
8.1 States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
8.2 Changes by Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Abstract

Following the general concepts of the paper ’AAI – Actor-Actor Interaction. A Philosophy of Science View’ from 3.Oct.2017 this paper illustrates a simple application where the difference as well as the
interaction between an actor story and several actor models is shown. The details of interface-design as well as the usability-testing are not part of this example.(This example replaces the paper with the title
’AAI – Case Study Actor Story with Actor Model. Simple Grid-Environment’ from 15.Nov.2017). One special point is the meaning of the formal expressions of the actor story.

Attention: This toy example is not yet in fully conformance with the newly published Case-Study-Template

To read the full text see PDF

Clearly, one can debate whether a ‘toy-example’ makes sens, but the complexity of the concepts in this AAI-approach is to great to illustrate these in the beginning  with a realistic example without loosing the idea. The author of the paper has tried many — also very advanced — versions in the last years and this is the first time that he himself has the feeling that at least the idea is now clear enough. And from teaching students it is very clear, if you cannot explain an idea in a toy-example you never will be able to apply it to real big problems…

 

AAI – Actor-Actor Interaction. A Philosophy of Science View

AAI – Actor-Actor Interaction.
A Philosophy of Science View
eJournal: uffmm.org, ISSN 2567-6458

Gerd Doeben-Henisch
info@uffmm.org
gerd@doeben-henisch.de

PDF

ABSTRACT

On the cover page of this blog you find a first general view on the subject matter of an integrated engineering approach for the future. Here we give a short description of the main idea of the analysis phase of systems engineering how this will be realized within the actor-actor interaction paradigm as described in this text.

INTRODUCTION

Overview of the analysis phase of systems engineering as realized within an actor-actor interaction paradigm
Overview of the analysis phase of systems engineering as realized within an actor-actor interaction paradigm

As you can see in figure Nr.1 there are the following main topics within the Actor-Actor Interaction (AAI) paradigm as used in this text (Comment: The more traditional formula is known as Human-Machine Interaction (HMI)):

Triggered by a problem document D_p from the problem phase (P) of the engineering process the AAI-experts have to analyze, what are the potential requirements following from this document, all the time also communicating with the stakeholder to keep in touch with the hidden intentions of the stakeholder.

The idea is to identify at least one task (T) with at least one goal state (G) which shall be arrived after running a task.

A task is assumed to represent a sequence of states (at least a start state and a goal state) which can have more than one option in every state, not excluding repetitions.

Every task presupposes some context (C) which gives the environment for the task.

The number of tasks and their length is in principle not limited, but their can be certain constraints (CS) given which have to be fulfilled required by the stakeholder or by some other important rules/ laws. Such constraints will probably limit the number of tasks as well as their length.

Actor Story

Every task as a sequence of states can be viewed as a story which describes a process. A story is a text (TXT) which is static and hides the implicit meaning in the brains of the participating actors. Only if an actor has some (learned) understanding of the used language then the actor is able to translate the perceptions of the process in an appropriate text and vice versa the text into corresponding perceptions or equivalently ‘thoughts’ representing the perceptions.

In this text it is assumed that a story is describing only the observable behavior of the participating actors, not their possible internal states (IS). For to describe the internal states (IS) it is further assumed that one describes the internal states in a new text called actor model (AM). The usual story is called an actor story (AS). Thus the actor story (AS) is the environment for the actor models (AM).

In this text three main modes of actor stories are distinguished:

  1. An actor story written in some everyday language L_0 called AS_L0 .
  2. A translation of the everyday language L_0 into a mathematical language L_math which can represent graphs, called AS_Lmath.
  3. A translation of the hidden meaning which resides in the brains of the AAI-experts into a pictorial language L_pict (like a comic strip), called AS_Lpict.

To make the relationship between the graph-version AS_Lmath and the pictorial version AS_Lpict visible one needs an explicit mapping Int from one version into the other one, like: Int : AS_Lmath <—> AS_Lpict. This mapping Int works like a lexicon from one language into another one.

From a philosophy of science point of view one has to consider that the different kinds of actor stories have a meaning which is rooted in the intended processes assumed to be necessary for the realization of the different tasks. The processes as such are dynamic, but the stories as such are static. Thus a stakeholder (SH) or an AAI-expert who wants to get some understanding of the intended processes has to rely on his internal brain simulations associated with the meaning of these stories. Because every actor has its own internal simulation which can not be perceived from the other actors there is some probability that the simulations of the different actors can be different. This can cause misunderstandings, errors, and frustrations.(Comment: This problem has been discussed in [DHW07])

One remedy to minimize such errors is the construction of automata (AT) derived from the math mode AS_Lmath of the actor stories. Because the math mode represents a graph one can derive Der from this version directly (and automatically) the description of an automaton which can completely simulate the actor story, thus one can assume Der(AS_Lmath) = AT_AS_Lmath.

But, from the point of view of Philosophy of science this derived automaton AT_AS_Lmath is still only a static text. This text describes the potential behavior of an automaton AT. Taking a real computer (COMP) one can feed this real computer with the description of the automaton AT AT_AS_Lmath and make the real computer behave like the described automaton. If we did this then we have a real simulation (SIM) of the theoretical behavior of the theoretical automaton AT realized by the real computer COMP. Thus we have SIM = COMP(AT_AS_Lmath). (Comment: These ideas have been discussed in [EDH11].)

Such a real simulation is dynamic and visible for everybody. All participating actors can see the same simulation and if there is some deviation from the intention of the stakeholder then this can become perceivable for everybody immediately.

Actor Model

As mentioned above the actor story (AS) describes only the observable behavior of some actor, but not possible internal states (IS) which could be responsible for the observable behavior.

If necessary it is possible to define for every actor an individual actor model; indeed one can define more than one model to explore the possibilities of different internal structures to enable a certain behavior.

The general pattern of actor models follows in this text the concept of input-output systems (IOSYS), which are in principle able to learn. What the term ‘learning’ designates concretely will be explained in later sections. The same holds of the term ‘intelligent’ and ‘intelligence’.

The basic assumptions about input-output systems used here reads a follows:

Def: Input-Output System (IOSYS)

IOSYS(x) iff x=< I, O, IS, phi>
phi : I x IS —> IS x O
I := Input
O := Output
IS := Internal

As in the case of the actor story (AS) the primary descriptions of actor models (AM) are static texts. To make the hidden meanings of these descriptions ‘explicit’, ‘visible’ one has again to convert the static texts into descriptions of automata, which can be feed into real computers which in turn then simulate the behavior of these theoretical automata as a real process.

Combining the real simulation of an actor story with the real simulations of all the participating actors described in the actor models can show a dynamic, impressive process which is full visible to all collaborating stakeholders and AAI-experts.

Testing

Having all actor stories and actor models at hand, ideally implemented as real simulations, one has to test the interaction of the elaborated actors with real actors, which are intended to work within these explorative stories and models. This is done by actor tests (former: usability tests) where (i) real actors are confronted with real tasks and have to perform in the intended way; (ii) real actors are interviewed with questionnaires about their subjective feelings during their task completion.

Every such test will yield some new insights how to change the settings a bit to gain eventually some improvements. Repeating these cycles of designing, testing, and modifying can generate a finite set of test-results T where possibly one subset is the ‘best’ compared to all the others. This can give some security that this design is probably the ‘relative best design’ with regards to T.

Further Readings:

  1. Analysis
  2. Simulation
  3. Testing
  4. User Modeling
  5. User Modeling and AI

For a newer version of the AAi-text see HERE..

REFERENCES

[DHW07] G. Doeben-Henisch and M. Wagner. Validation within safety critical systems engineering from a computation semiotics point of view.
Proceedings of the IEEE Africon2007 Conference, pages Pages: 1 – 7, 2007.
[EDH11] Louwrence Erasmus and Gerd Doeben-Henisch. A theory of the
system engineering process. In ISEM 2011 International Conference. IEEE, 2011.

EXAMPLE

For a toy-example to these concepts please see the post AAI – Actor-Actor Interaction. A Toy-Example, No.1