3

Knowledge Systems

3.1. Introduction

In this chapter, systems of knowledge are introduced as a second pillar of systems engineering. In the previous chapter, we characterized technological systems as artificial systems with two essential traits: (1) they are developed and operated to provide services to persons (this is their purpose) and (2) they are designed and produced using the scientific and technological knowledge needed to ensure that this goal will be achieved. Thus, systems of scientific and technological knowledge form one of the key levers which allow engineers to carry out their task of developing technological systems that meet defined goals. Systems of knowledge are therefore the central part of technological systems engineering. This is why we will define, in the following, what we understand by scientific and technological systems of knowledge, and how this knowledge is integrated into the process of systems engineering.

3.2. Knowledge and its bearers

We assert that knowledge does not exist separately, nor does motion¹. What exists are individuals who have knowledge, just as there are bodies in motion. This will be our initial assumption. In other words, in this chapter and throughout this book, knowledge does not refer to any world of ideas, such as the one attributed to Plato by a long philosophical tradition or even the one proposed by K. Popper who, in [POP 72], postulates the existence of a third world, i.e. that of objective knowledge, along with physicochemical phenomena (world 1) and that of knowledge, essentially subjective psychic activity (world 2).

We are not adopting the idea that knowledge might reside in books, models or any other form, such as databases of knowledge or other “ontologies” which are the objects of study for knowledge engineering experts [RUS 13]. In fact, we claim that these artifacts are representations which have value only for groups of individuals sufficiently educated to understand them; otherwise, they are completely worthless. Without Champollion and Egyptologists, the Rosetta stone would only be a beautifully crafted block of granodiorite bearing no historical knowledge. We will deal with the connection of knowledge with systems of signs in Chapter 4, which is dedicated to semiotic systems and in particular to models.

If individuals are the only bearers of knowledge, where does this knowledge reside? Along with neuroscientists, from D. Hebb [HEB 49], J.P. Changeux [CHA 97], G. Rizzolati [RIZ 05] or M. Gazzaniga [GAZ 09], we will say that the brain is the organ of knowledge. To know is one of the brain’s dispositions, with that of feeling emotions (love, hate and fear). To be more specific, the neocortex is the part of the brain (80% of the human brain) whose plasticity allows us to “engram” knowledge.

This disposition to know is actualized through learning during which the individual often interacts with others, particularly during early learning (the child learns to walk, speak with relatives), even if, according to Spelke [SPE 07], we assume that infants have an innate capacity to acquire core knowledge. During this learning phase, networks of neurons will be formed, which neuropsychologists have called “engram” [LAS 50], “cell assembly” [HEB 49] or even “pexgo” [BIN 76]. These maps are the material basis of cognitive processes whose purpose is to acquire knowledge by shaping a previously uninformed or differently informed neuronal system: walking, playing violin, demonstrating or memorizing a theorem are, therefore, embodied cognitive processes. These cognitive processes are the activity of these systems of neurons during their formation, when knowledge is acquired, and then formed, when this acquired knowledge is used. The repeated summoning of knowledge reinforces bonds inside these systems of neurons. It also facilitates the adjustment or reorganization of this knowledge by the association and reorganization of neuronal systems due to the neocortex plasticity. Inversely, lack of use may lead to the unlinking of these neuronal systems, that is to say, forgetfulness. Damage to these neuronal systems may also lead to a loss of knowledge, such as in the case of aphasia [LUR 76].

This biological underpinning of knowledge allows us to propose the following classification:

Therefore, knowledge is a biopsychological object, due to their location and the biochemical nature of the processes involved. We can refer to individual or subjective knowledge, since they are first “engrammed” by the individuals involved. This knowledge evolves throughout the life of the individual. If K_i(t₁) is the total knowledge of an individual, i is instant t₁; then at instant t₂, K_i(t₂)= K_i(t₁)+AK_i(t₂-t₁)-FK_i(t₂-t₁), where AK_i and FK_i represent the knowledge acquired and forgotten during the interval t₂-t₁.

When we refer to a given piece of knowledge, we can abstract its result by equating the multiplicity of cognitive processes activated by an individual at different moments or several individuals corresponding to this piece of knowledge.

3.3. Intersubjective knowledge

Due to the way they are acquired, pieces of knowledge are also social objects. In fact, early learning (procedural and conceptual) for a very young child occurs through high emotional closeness to relatives; further learning, whether at school or work, occurs most often when in contact with teachers or peers. This interaction with teachers or peers allows the individual to adjust personal knowledge to that of others, to refine them, correct them and confirm them in a continuous validation process. Researchers have already described these mutual learning phases, during which stakeholders, of a company or a team, form a distributed cognitive system and adjust their subjective knowledge and produce shared or inter subjective knowledge [HUT 96, AUV 09]. Since G. Rizzolati discovered “mirror” neurons in different animals, and more recently in humans, we consider that this intersubjectivity also has a neuronal basis. These “mirror” systems play a key role in empathic phenomena which are a condition favoring the learning process.

In this neurosociological framework, we can refer to knowledge of a given social group S such as a family, a village, a business team [ENG 98], a company [SIM 91] and, more broadly, a society as the total knowledge shared by the individuals in this system.

3.4. Concepts, propositions and conceptual knowledge

Conceptual knowledge (know-what) is of particular interest to us within technological systems engineering, even though procedural knowledge (savoir-faire or know-how) has a key role in tuning phases in the development of a system.

The elementary piece of conceptual knowledge, referred to in the statement “S knows p”, is the proposition designated by the statement p. A proposition, itself, is an abstract system composed of concepts², which are the components of any construct (propositions, theories, bodies of knowledge, etc.), just like elementary particles form the basis of any concrete object. Concepts may be extra-logical concepts: constant, such as that designated by the sign “Pollux” or collections such as that designated by “satellite” which form predicates such as those designated by “is a satellite” or “belong to the category of satellites”, or logical concepts such as those designated by “not”, “all”, “entails”. Thus, the proposition designated by the statement “Pollux is a satellite of Saturn” consists of two constant concepts designated by “Pollux” and “Saturn” and a predicate designated by “is a satellite of”. Logical concepts form the endo-structure of a proposition. Its environment as a system provides a context to the proposition and its exo-structure is made up of all the connections that the proposition holds with the objects in its environment. Surrounding objects may be other constructs (concepts, propositions, theories, bodies of knowledge, etc.) but also the concrete objects and facts to which they refer. In particular, in scientific or technological propositions, connections to concrete objects and facts are designated as “semantic assumptions”. When a proposition does not refer to any concrete object or fact, it is a formal statement and, in the opposite case, it is a factual statement (about facts).

The meaning M of a concept c or of a statement p, in a given context, has two components: first, its extension, i.e. the total referents R (all concrete and abstract objects that are referred to), and, second, its intension or content C, namely, the set I of propositions implied by c (or by p) and the set P of proposition implying c or p.

In a defined context, a proposition may or may not have a meaning. It is meaningful when its intension is not empty (i.e. with antecedents or consequents), whereas it is meaningless when its intension is empty (i.e. without antecedent and consequent). As an example, the proposition “the specification S is validated”³ is meaningful in the context of the ARP4754A standard since it is connected with propositions such as “a requirement is validated when it is sufficiently correct and complete” or even “a specification S is a set of requirements and assumptions related to a system type Σ”, whereas the following one “the system type Σ specified by S is validated” is meaningless in the same context.

Now, if we consider a context C including the proposition p, the context Citself forms a system whose composition is a set of propositions. These propositions are linked together by relationships such as inference relationships. This system has an environment composed of other systems such as formal systems: logical, mathematical, etc. The scientific and technological systems are characterized by the richness of their interdependencies (open systems), whereas pseudo science and the magical thoughts are distinguished by their self-sufficiency and isolation vis-à-vis other areas of knowledge (closed systems).

3.5. Objective and true knowledge

Among the conceptual knowledge shared by a social group, some cannot be subjected to any conceptual verification process (e.g. a formal demonstration) or empirical verification process (e.g. an experiment). This is a type of knowledge that cannot be corroborated or falsified according to Popper [POP 02].

Quite the reverse, a piece of objective knowledge is a piece of knowledge that is able to be corroborable or falsifiable through a verification process that can be conceptual (a formal demonstration) or empirical (an experiment). The use of test apparatuses allows⁴ or would allow⁵ us to carry out verification procedures. The result of this verification will either confirm or refute the concerned piece of knowledge. When an insufficient amount of evidence is only collected, an objective piece of knowledge remains as an assumption⁶.

Thus, propositions designated by statements such as “the Earth is round”, “when the volume v is constant, the pressure p of a constant quantity of gas is proportional to its absolute temperature T” or even “light propagates in a medium called the luminiferous ether” are objective knowledge, in the sense that verification devices have been defined, which can either confirm or refute this knowledge when put to the test. This is, for example, the case for experiments carried out by Charles and Gay-Lussac which confirmed Charles law that linked the pressure and temperature of a gas at a constant volume; however, the Michelson and Moreley experiment refuted this assumption of the luminiferous ether. Therefore, inter subjective knowledge can be classified into two categories: objective or unverifiable knowledge. Systems engineering cannot rely on unverifiable knowledge.

Finally, some objective knowledge may be said to be true, such as the proposition designated by: “in the field of complex numbers, any algebraic equation of nth degree has exactly n solutions”⁷ or even “the Earth is round”⁸. However, these two statements are not equally true. The first statement, which is involved in an abstract system, is true in formal terms; it is a truth of reason (or a formal truth), whereas the second statement is related to a concrete object. The truth, associated with this type of propositions about real things and facts, is a truth of fact⁹, which comes by degrees. The Earth is only round as a first approximation and the associated proposition is only partially or approximately true.

Establishing the formal truth of an abstract proposition or the factual truth of factual proposition is not done in the same way. The first is based on coherence, the coherence of the proposition, for which we wish to establish the formal truth with respect to its premises, whereas the second is based on the consistency of the factual proposition with the corresponding facts.

With regard to the factual truth of a proposition, it comes from the concordance between this factual proposition, its antecedents and consequences, with the corresponding facts. Thus, an individual has a true perception of a circular figure if, in fact, he/she perceives a circle when a circular figure is presented. An additional piece evidence was provided, when observing the activity of certain neuronal systems, an experimenter (neuroscientist) determined, rather precisely, what was perceiving the individual ([KRE 00], cited in [BUN i0]). Moreover, the consistency of cognitive processes with associated facts is only approximate. Consequently, we can assign only a partial truth value to a factual proposition.

3.6. Scientific and technological knowledge

Bunge [BUN 10] inserts the systems of scientific and technological knowledge into the following classification:

Figure 3.1. Conceptual knowledge classification

Depending on whether the purpose of this research is the only constitution of knowledge or another utility, these theories fall under fundamental sciences (autotelic systems) or applied sciences (heterotelic systems).

3.6.1. Fundamental sciences

The ultimate purpose of factual fundamental sciences is to discover, in the form of nomological propositions, the laws that link together the facts of a domain. The scientific approach involves defining the concepts that identify the essential properties of concrete systems (physical, chemical, biological, psychic and sociological) to represent, in the form of assumptions, laws that link these properties together. These assumptions are organized into theories, that is to say, in the form of hypothetico-deductive systems which, using basic postulates, derive theorems that can be deduced logically. These assumptions are then corroborated or refuted as scientific laws (nomological propositions) via a verification process which establishes whether a nomological proposition is or is not consistent with the referred facts. The verification process includes tools, protocols and observational and experimental data.

Depending on whether these nomological propositions link only observable properties or both observable and non observable properties, these law propositions will only be predictive in the first case or will have an explicative value in the second case. For example, propositions of thermodynamics are predictive propositions which help predict the evolution of a fluid with regard to the variation in one of its essential properties, but they are not able to explain this evolution. However, the kinetic theory of gases proposes, for the same facts, a construction that helps us to understand and explain this evolution.

A nomological proposition is an abstract system, i.e. a fiction, an abstraction of individuals’ own cognitive processes. It is only accessible and sharable by means of systems of signs such as L(x1, ..,, x_n, c₁, ..c_p), expressed in a natural or artificial language such as mathematics: L(x₁, ..,, x_n, c₁, ..c_p) associated with semantic assumptions {SA_i(xi)}. The couple L(x₁, ..,, x_n, c₁, ..c_p) associated with the assumptions {SA_i(xi)} is a law statement. The way in which the nomological propositions are designated by law statements will be the focus of the next chapter.

Before discussing the truth value of a nomological assumption, one must first question its meaning. As described previously (section 3.4), the meaning of a proposition is formed, on the one hand, from the reference class of the proposition (e.g. gaseous matter, fluids and ultimate components of matter) and, on the other hand, from the intension of this proposition (its antecedents and consequences). The meaning of a proposition precedes its truth; this implies that only meaningful propositions may have a truth value. It is then possible to attach a truth value to a meaningful nomological proposition.

A nomological proposition only ever partially represents a factual law to the extent that such a proposition can only have an approximate truth value. The van der Waals gas law is only approximately true, but its truth value is greater than that of the ideal gas law.

For an assumption to be considered as a nomological proposition that is at least partially true, there must be a sufficient amount of empirical evidence confirming it. This evidence may result from direct or indirect observations or experiments.

Thus, the existence of Neptune, predicted by Le Verrier and introduced to confirm Newton’s theory of gravity, required direct evidence such as the direct observation of Neptune by Johann Galle.

Similarly, the existence of the Higgs boson, introduced into the standard model of elementary particles to explain the diffraction of electroweak interactions, required even more indirect evidence insofar as its existence would be too short-lived to detect it and only the products of its disintegration would be observed. Detecting these products of disintegration, therefore, is a truth indication of the nomological proposition concerning the existence of Higgs boson.

3.6.2. Applied sciences and technology

The purpose of applied factual sciences and technology is to provide resources to act upon the real world, which are efficient since they are consistent with factually true law statements (approximately) and they are rationally based and rationally justified. This is what distinguishes factual applied sciences and technology, one the one hand, from fundamental sciences (as an autotelic activity) and, on the other hand, from techniques which resort to experience and routine without any other form of justification, as the philosopher Alain [CHA 60] expressed as follows: “What is the peculiarity of this technical thought? It is that it tries with hands instead of seeking through reflection”.

Technology bears two aspects of fundamental and applied sciences: first, the scientific method that provides operative technological theories and, second, results of applied sciences that provide substantive technological theories.

3.6.3. Operative technological rules

Operative technological theories are applications of the scientific method to action, in other words, scientific theories for action. What first characterizes these operative technological theories is to present them as problem-solving processes, which go from stating the problem to be solved to the verification of a solution. Then, it resorts to mathematics and logic by means of theories such as theories of value, scheduling, games, linear programming or even queues. Finally, this is the lack of reference to particular factual sciences (physics, chemistry, biology, psychology and sociology). The operative technological theories apply to any type of objects without special consideration of manipulated objects.

Operations Research is the archetype of these operative technological theories. So, in [CHU 61, p. 13], Churchman et al. describe the different stages of an operations research project as a series of rules, including:

We can easily observe similarities between this method and the one recommended by the mathematician George Polya in his book How to Solve It? [POL 45] (in other words, how to formulate and solve a problem?), which is a heuristic method of mathematics based on problem-solving approach:

As we will see in the second part of this book, systems engineering methodologies fall completely into this category of operative technological theories.

3.6.4. Substantive technological rules

Substantive technological theories are derived from results of factual scientific theories (physics, chemistry, biology, psychology and sociology) into technological rules. In fact, what substantive technological theories do is they derive various technological rules from nomological propositions. Then, these rules can be used in different phases of action. Flight mechanics theories for airplanes or helicopters are derived from fluid mechanics as a fundamental science.

Engineers developing technological systems mainly base their action model on substantive technological rules.

These substantive technological rules are derived from nomological propositions such as the one in the following example, relating to the lift law of a wing (which is already included in applied science). This law is expressed by the formula: F_Z = 1/2ρV²SC_z. From this, we can deduce the following technological rules:

Regarding the nomological proposition from which they derive, these technological rules introduce an asymmetry between the intended effect (the property of the object that we seek to control) and the means used (the property of the object on which we will act) to meet this goal, while nomological propositions are symmetric (acausal). These technological rules become the components of reasoning process implemented in the design framework [MIC 06] .

Finally, it must be noted that if truth is the most important property of a scientific proposition, the efficiency of a technological rule prevails over its degree of truth. A technological rule T₁ derived from nomological proposition L₁ may be more efficient than a technological rule T₂ derived from nomological proposition L₂ whereas L₁ is less true than L₂ (i.e. L₁ provides less precise predictions than L₂). The most efficient technological systems do not necessarily use the most accurate scientific theories.

3.7. Knowledge and belief

To bring this chapter on knowledge systems to an end, we will describe the relationship between belief and knowledge. In fact, an engineer is constantly making decisions (about specifications, design, implementation and verification). Once they are made, he/she generally believes that these decisions are the best decisions or the less bad decisions possible in a given situation. If he/she wants to justify them, he/she refers to a certain amount of scientific and technological knowledge, confirmed for the first and efficient for the second.

Also, we recap the way in which Bunge [BUN 83] connects the concepts of knowledge and belief¹².

According to Bunge, if p is a nomological proposition, we can say that an individual s:

Also, for a technological rule r, we can say that an individual s:

As a critical and reflective engineer (expression from [SCH 83]), he/she must therefore respond to the question of whether he/she is justified to believe to the substantive and operative technological rules on which his/her design reasoning is based.

We will see that the validation process, as described in Chapter 8, is a process which gives us evidence to believe that correctly validated specifications are also as exact as possible, provided that it is conducted as rigorously as required.

Similarly, we will see that the verification process, as described in Chapter 9, is a process which gives us evidence to believe that correctly verified systems are also as consistent as possible with the specification, provided that it is conducted as rigorously as required.

1 Knowledge as Motion are reifications, i.e. errors of treating as a concrete thing something which is not concrete, but merely an idea (A.N. Withehead).

2 It is at the expense of a word game, on which is a concept, that the C-K theory could arrange concepts and knowledge into two distinct spaces [HAT 03].

3 Refer to the second part of this book, Chapter 5.

4 This is the case of the interferometer of Michelson.

5 This is the case of the VIRGO gravitational wave detector near Pisa, Italy.

6 This is the case for gravitational waves, whose existence was predicted in 1918 based on Einstein’s general theory of relativity and, for which, impressive experiments are still ongoing (VIRGO and laser interferometer gravitational-wave observatory (LIGO)) or under preparation new gravitational wave observatory (NGO).

7 Gauss provided evidence of its truth in the form of four distinct demonstrations.

8 Its truth is based on observations and experiments, first the observation of moon eclipses, considered by Aristotle (On the Heavens) and us, as a valid proof of the rotundity of the earth. Other evidences followed with Eratosthenes, the Abbasid Caliph Al-Ma’mun of Baghdad, and in modern times with Magellan’s circumnavigation or the Apollo 11 trip around the moon, after an obscurantist episode in which some religious scholars, such as Lactance or Cosmas of Alexandria, imposed literal readings of the Bible to fight a science in loss of audience.

9 The difference between truth of reason and truth of fact was introduced by Liebniz (Theodicy, 1710).

10 Thus, the demonstration of G. Perelman for the Poincaré’s conjecture has been declared valid by the mathematical community after multiple verifications by his peers.

11 As an example, high lift devices implement this technological rule.

12 Usually hinged the opposite way, knowledge is, in the philosophical tradition, a true and justified belief (from a track of Plato’s Theaetetus where knowledge is considered as a “right opinion provided with reason”).