MCB

[published in: Internat. Journal of Intelligent Systems, Vol 12, Number 8, August 1998, p. 577-595]

A major advance in theoretical works on Artificial Intelligence has been distinguishing the knowledge and implementation levels, where the second is system-oriented whereas the first is "world-oriented". This so-called "knowledge-level" perspective - introduced by Allen Newell¹ in 1980 - has provoked a profound shift in Computer Science in general with consequences which about one decade later have led to an established new paradigm in knowledge engineering, now widely considered -- in theory -- as building a model in terms of knowledge, rather than as extracting expertise from an expert². A further major advance in the same domain has been recently supplied by Ford et.al.³ (p. 9) who claim that "human experts construct knowledge from their own personal experiences": consistent with this theoretical assumption they present knowledge acquisition (p. 10) as a "constructive modeling activity, and not simply a matter of 'information transfer'".

In contrast with this theoretical progress, the main streams of AI in general and of knowledge engineering in particular, although incompatible with the mapping paradigm of modeling, have not yet explicitely abandoned it; the physical symbol system hypothesis⁴ and the knowledge level theory ¹ for example, do not give explicit support nor critique to this paradigm but can do this only by ignoring two questions which - as this paper intends to show - are of central concern in a theory of knowledge and modeling: 1) What validates knowledge ? 2) Which is the relation between knowledge and reality ?

Within the mapping paradigm of modeling one presumes that the model is a copy, an abstraction, a representation of reality (copy-to-original relation between model and reality) and consequently defines model validation as checking the degree of correspondence between model and reality. This check would of course require that we compare our map of reality with reality itself. But firstly, as will be explained in detail later on, it is not necessary to assume that we have direct access to reality to evaluate the usefulness of a model and secondly this assumption creates an unsolvable dilemma, because it is impossible to compare our map (copy, abstraction, representation) of reality with reality itself. As von Glasersfeld ⁵ puts it (p.137): "It is impossible, because in order to check whether our representation is a 'true' picture of reality we should have to have access not only to our representation but also to that outside reality before we get to know it. And because the only way in which we are supposed to get at reality is precisely the way we would like to check and verify, there is no possible escape from the dilemma."

In the attempt to find a way out of this dilemma a central thesis of this paper is that "mapping" is not the way human minds work, and that we cannot know if our knowledge is "accurate" with respect to the ontic world: the best we can do - but it is pretty good, as Agnew et al.⁶ suggest - is to evaluate it with respect to its utility and viability (Ref.5 p. 134-142).

Recently constructivist paradigms have already been succesfully applied to knowledge engineerig both for the development of a new approach to the practice of reuse⁷ and as a theoretical foundation for knowledge acquisition (based on Kelly's personal construct psychology, see Refs.3 and 8). As Ford et.al.³ conclude (p. 27) "constructivist epistemology is a potentially rich set of ideas for those interested in developing computational models of human cognition and related systems for the assessment and representation of knowledge". This suggests that constructivism may be succesfully used also in developing new foundations for the practice of modeling. We further agree with Ford et.al.³ (p. 28) that one of the critical tasks facing the knowledge engineering research community is "to continue elaborating a variety of potential theoretical foundation for understanding the nature of expertise and the processes of modeling and representing knowledge".

A powerful constructivist theory of the human faculty of thinking, one which could best contribute in understanding the nature of expertise and the process of modeling - thus decisively supporting the development of human-centered AI systems -, can be found in Kant's work. In the light of Kant's theory of modeling⁹ it can be shown that the established explanations of modeling (theory, methodology) do not match the practice of modeling as carried out by working knowledge engineers (praxis). This paper presents an attempt to link knowledge engineering with Kant's theory in order to reduce this mismatch by means of a constructivist modeling paradigm (theory) for the engineering of AI software systems.

Modeling plays a fundamental role in Computer Science in general and in knowledge engineering in particular. As Rothenberg¹⁰ puts it (p.75): "Modeling is one of the most fundamental processes of the human mind. ...the quintessential human conceptual tool." Similarly, according to Top and Akkermans¹¹ (p.265): "the modeling approach is a major principle in the CommonKADS methodology". In the area of knowledge engineering, great efforts have been put forth as it is shown by the very widespread methods of object-oriented analysis, knowledge acquisition as modeling, KADS and other. Their main strength lies in the fact that modeling - which allows to adapt software systems to human thinking - plays a primary role in them (Refs.12, p.9 and 3, p.9). But the approach to modeling as well as the underlying approach to knowledge has not yet been questioned critically enough in these methods (with the exception of Ford et.al. ³ and related works): this is why, up to now, it has not yet been possible to exploit the main strength of these methods. Three quotations may exemplify the currently established approach to modeling in knowledge engineering:

In knowledge engineering the model is called knowledge base and can be viewed as being composed mainly of so-called facts and rules. As the examples show, in the established approach modeling is conceived as a finding, picking up and mapping of states of affairs ("Sachverhalte") which exist independently of us. Lusti¹⁵ expresses it explicitly in the following way (p.17): "The real world is made of objects and their relations. The corrspondent symbolic world is made of object symbols and of relational symbols."

For these authors, modeling is merely the "finding, picking up and mapping" of objects (including events, relations, etc.) that are waiting for us ! But, if objects, events and relations are merely waiting to be found, picked up and mapped, then this necessarily implies the hypothesis that we can directly acces the order of things which exists independently of us (call it "ontic order") and derive from it the order of things which is embodied in our knowledge (call it "derived order"). And because the ontic order is independent of us then also the derived order will be assumed - within some admitted limits of incompleteness and distortion - to be independent of us, hence universal and valid for everybody¹⁶. This theoretical position entails or at least grounds the conviction that a good model must correspond to that independent order of things in the same way as a good picture corresponds to its original: that is, it must have a direct, bi-unique correspondence with the ontic order. If this mapping and correspondence theory of modeling is used in software engineering, that is in the modeling relationships between developer, user and software system, then this yields the following implicit requirements to modeling:

A critical review of the practice shows on the contrary that with current knowledge engineering methods we do not succeed in fulfilling these 3 requirements. Each of the 3 relationships presents us with a huge modeling gap:

This shows that knowledge engineering methods cannnot yet fulfill their aim, which consists in making systems possible which are adapted to the human faculty of thinking, and it leads to presume that one of the main methodological reasons for this lies in finding, picking up and mapping as a modeling approach.

In knowledge engineering "modeling" can be viewed as the activity of producing a model of expertise with the purpose ¹⁰ of building software models (called "knowledge-based systems") able to perform at the expert's level of knowledge and skills (relation of the model to the system represented). The activity of producing the model is usually called "knowledge representation" or "knowledge modeling" and its result may be referenced as "knowledge-level model"¹⁷. This model of expertise - a minimal formalisation (representation) of the domain expert's skilled performance and knowledge (Ref. 18, p.53) - has been usually expressed in practice in terms of two knowledge categories, domain knowledge and control knowledge, that Clancey¹⁹ specifies as a model of some system in the world and a model of reasoning processes (p. 34). A more refined approach further divides control knowledge in three independent categories: inference, task and strategic knowledge¹⁷. These categories distinguish different types of conceptual models (Ref.20, p. 164) classified in terms of different roles that knowledge can play in reasoning processes as well as different construction, design and implementation activities. The main activity in the construction of these conceptual models is called conceptualisation and the main operands involved in this process are objects, concepts and predicates.

From this brief sketch it is clear that any research program in knowledge engineering must necessarily address and/or be based on assumptions about the topics of modeling, software models, knowledge representation, conceptualisation, objects, concepts and predicates. In fact, within the currently dominant research programs, we may distinguish a number of questions and assumptions - both explicit and implicit - related to these topics. They are ubiquitous among computer scientists and place decisive constraints on a theory of modeling and expertise but are almost never expressed:

As the answers to these fundamental questions clearly show, what knowledge engineers assume delineates the essential characteristics of a "mapping & correspondence theory" which suffers from problems like contraditictions (2.), tautologies (4.), inconsistencies (6.) and, more generally, claims that the theory can not support.

Modeling has become central to knowledge engineering. Thus, if human-centred software systems have to be developed, i.e. systems which are as much as possible adapted to our faculty of thinking, a new modeling approach must be devised. The foundation of the new modeling approach proposed here was formulated already more than 200 years ago by Kant⁹ in his "Critique of Pure Reason" as follows: "Hitherto it has been assumed that all our knowledge must conform to objects. But all the attempts to establish something a priori about objects by means of concepts, ..., have, on this assumption, ended in failure. Let us therefore make trial whether we may not have more success ... if we suppose that objects must conform to our faculty of knowing." (B XVI).

[A note on references: Citations to the Critique of Pure Reason⁹ (also abbreviated as Critique) omit for simplicity to repeat the reference number and are located in the customary manner by reference to the pagination of Kant's first ("A") and second ("B") editions.]

For the purposes of this paper Kant's suggestion to suppose that objects must conform to our faculty of knowing constitutes the gateway to his Critique. The basic knowledge hypothesis which can be derived from it is as follows:

This position approaches Ernst von Glasersfeld's "Radical Constructivism"^5,24,25 with its distinction between "ontological reality" and "experiential reality", where the relation between the two can be stated as follows: ontic reality delivers the raw material out of which our knowledge processing system constructs objects, events, relations, etc. i.e. experiential reality (the order of things embodied in our knowledge). Thus, the relation between reality and knowledge is no longer an original-to-copy relation but a material-to-product relation. Von Glasersfeld²⁴ (p.16) further specifies this material-product relation by showing that the product (knowledge) can not "represent" reality (the raw material), instead it must prove to be valid by a "functional fit", that is by allowing us to attain the goals we happen to have chosen. In the light of Kant's theory of knowledge, von Glasersfeld's specification of the relation between reality and knowledge contributes to the following assumption:

By means of the previous two hypotheses the three examples of the established approach to modeling could be reformulated in a constructivist way as follows:

The modeling approach proposed here - called "viability-oriented modeling" in honour to von Glasersfeld⁵ who has introduced the notion of viability in modern epistemology (p. 134-142), considers facts and rules of a knowledge base as working formalizations of "states of affairs" and these states of affairs as "viable constructs", i.e. as something that we make (construct) ourselves through our thinking, through the organisation of our interactions with the environment in a way which allows us to achieve our goals (viable way).

Based on Newell's paradigm of a knowledge level¹ in an earlier research on Human Information Processing we had proposed a distinct "operations" level - lying immediately below the higher functions level - which is characterized by "mental operations" as the medium and the principle of "operational constitution" as the law of behavior²⁶. This "operations level hypothesis" was the result of interpreting Silvio Ceccato's^27-31 pioneering contributions to Artificial Intelligence from the point of view of knowledge engineering. An important feature of the basic mental functions which implement the "operations level" is that they provide an abstract description of mechanisms required for the "creation" of knowledge, where "creation" means that the responses to a stimulus depend more on the operations established and applied by the subject than on the operations imposed to the subject by the imputs.

The need of a stronger basis in knowledge theory for the claims of this research on one side and the identification of possible arguments for these claims in Kant's work on the other side, led in the following years to various attemps at linking Knowledge Engineering to Kantian philosophy. This research included a system model of Kant's architecture of the mind,³² the integration of Kant's theory of mental activity with Ceccato's model of mental operations,³³ reflections on a new methodology of knowledge representation,^34,35 suggestions on how to overcome with Kant the software crisis³⁶ and a refined model of Kant's theory of knowledge composed of 3 parts: an interpretation of Kant's new language, an architecture of knowledge processing units and a hierarchy of knowledge components³⁷.

Many results in this work suggested that Kant gives in his theory of knowledge⁹ a systematic treatement of fundamental questions of modeling, i.e. of questions that place a number of decisive constraints on the assumptions underlying a theory of modeling and expertise for knowledge engineering.

Long before publishing his famous work in 1781, Kant had conceived its purpose in the answer to a question which is probably the most fundamental question of modeling: on which ground is founded the relation between the construction in us ("Vorstellung in uns") and the object [Letter to Markus Herz, dated 21. Febr. 1772]. The Critique presents Kant's attempts at answering this question³⁸. To this aim he adopted the method of investigating the faculties required for the performance of the basic cognitive tasks that produce constructions³⁹, devoting most of his research to develop (9 years) and correct (6 years) his answer to that question which was finally presented in the "Analytic of Concepts" (80 pages) and in the "Analytic of Principles" (180 pages), two relativly small parts of the whole "Critique of Pure Reason "(922 pages, 1787 edition B).

The well-known obstacles in understanding Kant's Critique of Pure Reason have been attributed to bad writing, inconsistencies, contradictions and confusion. Such deficiencies on the side of the author may in some case explain minor problems in making sense of what he writes but they cannot explain the major difficulties. These are grounded in the kind of operation he was performing⁴⁰: a conceptual revolution which proposed a new language - as Kant himself explains [Letter to Chrisitan Garve, dated 7. Aug. 1783] - but had to use traditional words for designating the new concepts. Part of this new language are for instance the highly structured and specialized meanings that Kant associates both with common german terms, like "Vorstellung" and "Anschauung" and with more philosophical terms, like "Mannigfaltige" and "a priori".

The first term, "Vorstellung" is usually translated as "representation". But this is "disastrous in epistemological contexts" (Ref.25, p. 94): in fact it can be highly confusing, especially if "representation" is interpreted in terms of something mapping reality, because then it would contradict Kant's fundamental assumption in the Critique. In line with von Glasersfeld's view that "The element of autonomous construction is an essential part of the meaning of Vorstellung" (Ref.25, p. 94) and consistent with recent proposals from Kantian research³⁹ instead of using the literal translation "representation" this term will be translated here by "construction" which both has a corresponding verb (to construct) and exhibits the same duality (the act of -ing / that which is -ed) like "representation".

The second term, "Anschauung" is usually translated as "intuition", but also this word, although the accepted translation even in current Kantian research, "is not altogether a satisfactory one" (Ref.41, p. 679). Our proposal⁴² is to translate it by "framing" in the sense of the result and the act of providing a skeletal spatio-temporal structure to the perturbations⁴³ which alter our sensory organs.

The third term, "Mannigfaltige" is translated as "manifold" and interpreted as "variety" (Ref.44, p.70) or "diverse elements": but this interpretation suggests something structured in terms of elements, whereas Kant's use points more in the direction of somenthing unstructured. We therefore suggest to interpret manifold as "an unstructured operand of a structuring operation".

The fourth term, "a priori" is often interpreted as "innate", particularly by non-philosophers who try to apply Kantian ideas within their domain of research. But recent research on Kant's notion of "a priori" has demonstrated that this interpretation is "disguised and unjustified" and proposed a sense structured in three components. Within our scope we will focus on a modification of the second of these sense components which "connects with Kant's interest in origins" (Ref.39, p. 16): as Kant himself repeatedly suggests, a concept a priori is not something "implanted in us from the first moment of our existence" (B 167) nor something abstracted from sensations but something acquired through the operating of mind itself: "acquisitus est ... ab ipsa mentis actione"⁴⁵. It is, succintely stated, an operational scheme.

4. Ten Principles

Kant's fundamental assumption about the relation between basic cognitive tasks and objects is contained in the passage (B XVI) previously quoted at the beginning of part III: instead of assuming that our knowledge must conform to objects, suppose that objects must conform to our functions of knowing. The conception of objects conforming to knowing should not be interpreted as idealism in the traditional sense of arguing that mind generates existence and of denying an independent reality. In fact, Kant explicitely rejected idealism (B 274), said of himself that he is an empirical realist (A 371), in the sense of accepting that to our constructions "corresponds ... something real in space" (A 375) and repeatedly made references to existence of things ("Dasein der Dinge"). The basic idea is that knowing makes objects possible not as far as their existence is concerned ("dem Dasein nach" (B 125)) but as far as our experience of order and regularity (A 125) is considered. What exists are sources of alterations in our sensory organs which determine a continuous flow of perturbations but these perturbations do not include the order and regularity that only can make an object out of them. This conception of objects conforming to knowing can be formulated more succintely in the following principle.

In the Introduction to the Critique Kant explains that the raw material of sensorial perturbations (sinnliche Eindrücke) must be worked up by our faculty of knowing in order to become that knowledge of objects which is entitled experience (B 1). In what consists this "working out" ? Does our faculty of knowing simply transform perturbations into knowledge ? Kant's solution is more elaborated: he assumes that in generating empirical knowledge our faculty of knowing adds to what we receive through sensorial alterations ("Eindrücke") a kind of knowledge - called a priori knowledge - which is absolutely independent of all experience. This raises the question of a priori knowledge: what is this knowledge, which role does it play in basic cognitive tasks, which functions are required for the performance of these tasks and which mechanisms can fulfill these requirements ?

In the Critique, where Kant investigates "the faculties required for the performance of basic cognitive tasks" (Ref. 39, p. 25), the foundations of his answers to these and related questions are exposed in a relatively small part of it called "Analytic of Concepts". In the introduction (B 90) Kant explains how he will conduct his analysis. His procedure will not be that of dissecting the content of concepts as usual in philosophical investigations; rather, he wants to apply a rarely attempted analytic procedure which consists in the dissection (modeling) of the faculty of the understanding itself. This modeling will be done in terms of functions able to both develop a priori concepts "on the occasion of experience" (B 91) and to apply them in other experiences "freed from the empirical conditions attaching to them" (B 91). Although these remarks are only introductory and procedural, their importance for a consistent interpretation is such that it is worth covering them by a principle.

Kant introduces his analysis of the faculty of understanding by showing that all acts of understanding may be reduced to judgements. He identifies the functions of thought fundamental to all knowledge as the logical functions of judgment and considers all judgments as functions of unity among constructions (B 92 ff.). From general (formal) logic Kant derives a systematic account (Table of Judgments) of these functions - for example the relational functions of categorical, hypothetical and disjunctive judgments - established by abstracting from all content of a judgment. But in his Analytic he wants to take into account also the material that is delivered from sensibility (manifold of sensibility) because this material is required for producing a content of knowledge (B 102). And if a material is required, then also a mechanism operating on this material must be required for providing judgments with content. What could be such a mechanism ? Kant calls it "synthesis" and this notion will play an absolutely central and prominent role in his model, as Kantian research - after the pioneering work of Wolff⁴⁴ - is beginning to recognize only in recent studies^39,46. Synthesis plays an essential role in knowing, Kant argues, because it is what provides our knowledge with empirical content: it is "that which first gathers the elements for (producing) knowledge and unites them to (make up) a certain content" (B 104-5) or, more precisely, it is the act (operation) of "putting different constructions together and of conceptualizing into one knowledge unit the manifold that constitutes them" (B 103). A simple principle expressing the key idea concerning what produces a content of knowledge is the following.

But what role does synthesis play in providing content for judgments and how does this synthesis work ? We have on the input side the material delivered from sensibility and on the output side a knowledge unit with content. The material consists in a manifold of sensorial alterations (in neurophisiological terms a mass or cluster of electrochemical impulses) mentally framed in terms of space and time (spatio-temporal manifold or framed manifold): Kant calls it "Mannigfaltiges der Sinnlichkeit a priori" or "Mannigfaltiges der reinen Anschauung a priori" (B 102-3). In line with his fundamental assumption of the active role that mind plays in the construction of our knowledge ("die Spontaneität unseres Denkens") he claims that this framed manifold must "be first gone through, taken up and connected in a certain way in order to make a knowledge unit out of it" (B 103). When he then goes on saying that "as regards content no concepts can first arise by way of analysis" his claim is that conceptual content (the content of any concept) arises through the synthesis not of predicates but of the spatio-temporal manifold. This can be covered by the following fourth principle.

Before concluding this introduction to the function of synthesis in general Kant assigns it to a functional unit of mind that he calls imagination and points out, that although "an indispensable function of mind, without which we would have no knowledge whatsoever, we are scarcely ever aware of it" (B 103). Later in the argumentation he repeats the same idea suggesting that we are not aware of the operation of connecting (B 130) and that we cannot prevent the "natural and inevitable illusion" of taking for ready-made and given what instead is the result of our own synthetic operations (B 353-5). These remarks on our awareness of synthesis, are important in relation to Kant's radically new conception of an object as something conforming to knowing: if synthesis plays a central role in explaining how objects conform to knowing and if we are both "scarecely aware of it" and victims of an "inevitable illusion" then it not surprising that Kant's fundamental assumption sounds so abstruse, "exaggerated and absurd" (A 127) to us. Thus we obtain the following fifth principle.

Having thus introduced his notion of synthesis, Kant proceeds to explain how the three operations of scanning a spatio-temporal manifold, taking up parts of it into elements and of connecting these elements (B 104-5) could be implemented. He conceives these three steps as a triple synthesis: a synthesis of the spatio-temporal manifold ("Synthesis der Apprehension"), the operation of reproduction ("Synthesis der Reproduktion") and the operation of giving unity to the constructions resulting from this synthesis ("Synthesis der Rekognition"). As for judgments, which are considered as "functions of unity among our constructions" (B 94), so also for the synthesis of a manifold, unity of its operations is required. That is, the current synthetic operation must be either integrated with the previous or be the first of a new synthetic unit and all operations must belong to discrete synthetic units or elements. But what could provide these functions of unity among constructions. Kant's solution to this problem constitutes one of the central and most controversial claims of the Critique. He claims that the same function that gives unity to the various constructions in a judgment also constitutes a concept (pure concept, called the "category") that gives unity to the various constructions resulting from the synthesis of the framed manifold. In this way he obtains the Table of Categories, which displays the fundamental concepts of thinking - for example the categories of relation, i.e. 1. subject-predicate, 2. ground-consequence and 3. element-community - each of which corresponds to modes of judgment (Table of Judgments). Expressing in one principle the explanation of the third operation of synthesis we obtain:

Continuing his analysis Kant points out that the notion (requirements and implementation) of synthesis developed so far (principles 3, 4 and 6) is not enough for supporting his assumption on how mind relates to objects (principle 1). In fact, one could still claim that knowing conforms to objects (B 125), the opposite of Kant's own claim, for instance arguing that the ready-made object controls or guides the synthesis of its corresponding construction in us. What is required now is that within the third operation of synthesis i.e. "connecting elements" (principle 4), the categories introduced as its implementation (principle 6) "must be recognised as a priori conditions of the possibility of experience" (B 127). In other words, Kant wants to demonstrate that and how the categories are required to "know anything as an object" (B 125). To reach this goal Kant engages in his most complex analysis of cognitive tasks (that he calls "Transcendental Deduction of the Categories" (B 124)) covering objects, concepts, experience and functions of knowing. Although this "Deduction" is widely recognised as the core of his theory of knowledge, his "deepest investigations into the nature and origin of knowledge" (Ref. 44, p.79), there is little consensus among Kant scholars about the interpretation and the success of the Deduction. Nevertheless recently some authors are beginning to recognise that this part of his work has important contributions to make to contemporary discussions within cognitive science and artificial intelligence^39,47.

Kant begins his analysis of experience, that is of how we know anything as an object (task) by specifying requirements for the stream of cognition and the relation between knowledge and physical object. In the stream of cognition, he claims, we must have "the consciousness that what we think is the same as what we thought a moment before" (A 103); without this "unity" in the series of constructions, the preceding construction "would in its present state be a new construction" and therefore both concepts and knowledge of objects would be "altogether impossible" (A 104). After a digression on the role of concepts (see next) Kant asks the question of the relation between knowledge (contents of constructions, conceptual content) and object ("Gegenstandsbezug") and answers it by rejecting the common notion of correspondence between knowledge and physical object "since except our knowledge we have nothing" (A 104) which we could compare with it. In place of correspondence he introduces a new view of objects - where an object is "viewed as that which prevents our knowledge from being haphazard or arbitrary" (A 104) - and a new view of their relation to knowledge, characterised by consistency and coherence (Ref.39, p. 71): "For in so far as the contents of constructions ["Erkenntnisse"] are to relate to an object, they also must agree with one another in a necessary way ..., that is they must have that unity which makes up the concept of an object" (A 104-5). But this unity necessarily required for conceiving an object, cannot be derived from objects (as physical entities), because what is given to our mental faculties is merely a manifold. This leads to the problem of connection of a manifold. Connection - in the sense of a consistent and coherent unity - "does not lie in the objects" (B 134) and so "can never come to us through the senses" (B 129): it must be performed by an act of the understanding and "we cannot think of anything as connected in the object which we have not ourselves previously connected" (B 130). In modern terms, our capacity of knowing objects is "not data driven in any simple or obvious way" (Ref.39, p. 80): it must be a goal driven faculty that consistently and coherently constructs its experience and itself as an organised whole like in Piaget's pioneering constructivist view that "The mind organises the world by organising itself" (Ref.48, p.311).

Given this analysis of the nature of objects and due to the fact, that "we have to deal only with the manifold of our constructions" - and hence have no direct access to physical objects as something distinct from knowledge - "we are in a position to say that we know the object when we have produced synthetic unity in the spatio-temporal manifold" (A 105). This introduction to the analysis of experience can be covered by the following principle.

But what implements this necessary "synthetic unity" and performs the operation of connecting ? Kant's solution is that only consciousness can impart unity to the manifold of constructions (A 103) - that is to the synthesis of it - and that consciousness does this by means of concepts. Thus "all knowledge requires a concept" and this "is always, as regards its form, something universal which serves as a rule" (A 106) for performing the operation of connecting. For example, in order to think a line as an object "I must draw it, and thus synthetically bring into being a determinate connection of the given manifold, so that the unity of this act is at the same time the unity of consciousness" (B 137-8): here, the concept of a line is what serves as a rule (procedure) for connecting (by drawing) and realising by this act the required consistency and coherence (synthetic unity) of a line (object) in our mind.

The role of concepts then, as the word itself suggests, is precisely that of being unifying functions of consciousness applied to constructions (mental patterns) which "are nothing to us, and do not in the least concern us if they cannot be taken up into consciousness" (A 116). This approach to concepts and consciousness has striking analogies with that used by Silvio Ceccato in his pioneering contributions to Artificial Intelligence where he assigned to attention a central role in his computer model of natural language processing^25,27-31. Thus we obtain the following eighth principle.

This said we are now in place for tackling the problem of a priori knowledge. The task of providing synthetic unity requires an a priori ground of unity such that connection be provided in accordance with universal and necessary laws: otherwise, Kant claims, the unity of synthesis "would be altogether accidental", "a crowd of appearances would occupy our soul and yet no experience could ever arise from them" and "all relation of knowledge to objects would fall away" (A 111). This means that the functions of synthesis (concepts) that permit experience must be universal. At this point Kant assumes that the categories - pure concepts a priori, see principle 6 - supply these universal functions, as "conditions of possiblity" of experience. His main argument for this claim, is connected with the unity of experience (experiential or mental unity), the fact that "There is one single experience in which all perceptions are constructed ..." (A 110). First of all, due to the synthetic nature of objects (principle 7), the objects of our experience "are merely in us ...". Secondly, all these objects in me must conform to mental unity (that Kant mainly calls "unity of apperception"), that is, they must be "determinations of my identical self", which is only another way of saying "that there must be a complete unity of them in one and the same apperception" (A 129). If now the possibility of objects as well as their connection (synthetic unity) and experiential unity "are to be met with only in ourselves" it follows that the functions of synthesis which provide such objects must "precede all experience" (A 130): they must be "a priori". This can be formulated more precisely as follows.

At this point Kant's arguments for demonstrating that "objects conform to knowing" have reached a first milestone: in the 'Analytic of Concepts' he has shown that categories are what makes objects conform to knowing; in the 'Analytic of Principles' he will then pursue the next milestone and show how categories can make this. Having reached that first milstone allows now an important conclusion concerning the problem of the validity of knowledge. Where lies the truth of the objects of our experience (i.e. that these objects are not mistakes, not illusions) ?

Kant's view on empirical truth is that it depends on the consequences of the involved objects and concepts: "In any knowledge of an object ... there is truth, in respect to consequences. The greater the number of true consequences that follow from a given concept, the more indications are there of its objective reality." (B 114). The objective reality of concepts consists in their application to the material delivered by sensibility (B 150-1) which results in the constitution of experiential objects; but when are consequences of these objects and concepts "true" ? In other words, what could be a sufficient criterion for their empirical truth? In line with the view of an object as a consistent and coherent unity (principle 7), Kant claims that "the coherent employment of understanding is a sufficient criterion of empirical truth" (B 679). Hence a concept has more or less objective validity, depending on its stronger or weaker "viability" (the higher or lower number of coherent consequences that follow from it). This leads to the problem of what determines this viability. With the demonstartion that categories are what makes objects conform to knowing, its solution is simple: because categories implement "the formal unity of experience" and "are the grounds of the possibility of knowing any object whatsoever in experience" they necessarily also "render possible all objective validity (truth) of empirical knowledge" (A 125, B 126). Thus the categories, although subjective conditions, are at the same time objectively valid (A 125-6): they determine the viability of empirical knowledge. Given this conclusion and in the light of Kant's view on empirical truth as viability and coherence of mental processing, we are now in a position to formulate the following principle.

The ten principles developed so far are intended to be representative of the core of Kant's theory of knowledge. They result from taking seriously two questions which are of central concern in a theory of knowledge and modeling but have been ignored in AI research up to now:

1) What validates knowledge ?

2) Which is the relation between knowledge and reality ?

As the principles show, in his Analytic of Concepts ⁹ Kant gives grounds for taking seriously these two questions and supplies in his answers arguments for moving modeling from a mapping & correspondence theory to a "coherence & viability theory" that could decisively support the development of human-centered AI systems.

Applying these principles in a "critique" of the foundations of knowledge engineering allows to answer some of its fundamental questions in a new and promising way:

These new answers propose, that what constitutes modeling (knowledge representation, conceptualisation, objects, concepts and predicates) is characterised by coherence and viability not by mapping and correspondence: thus, comparing these new answers with those established in knowledge engineering (see section II.b) proves that what knowledge engineers think they would do (theory), does not match what they actually do (practice).

The established theory of modeling in knowledge engineering is a mapping and correspondence theory. By linking knowledge engineering to Kant's theory of knowledge and in the light of von Glasersfeld's Radical Constructivism it has been shown that this paradigm is not powerful enough to cope with the engineering of AI software systems: in fact, its explanations (theory) do not match the doing of modeling by knowledge engineers (praxis). Kant's Critique of pure Reason entails a coherence and viability theory of modeling which can be used to develop a theoretical foundation for understanding the nature of expertise and the processes of modeling from a human-centred position and in a way which would contribute to reduce this mismatch. The main concern in this paper has been to show the direction we must travel in order to develop such a foundation.

Acknowledgements: I am grateful to Allen W. Wood (Philosophy Department, Yale University) for reading the manuscript and offering his amendments. I want moreover to thank Vladimir N. Bryushinkin (Philosophy Department, Kaliningrad University) for having invited me to present to internationally renowned Kantian scholars some of the ideas which are central to this paper and for translating them into russian^34,36. Finally, I am deeply indebted to Silvio Ceccato and Ernst von Glasersfeld for having given me inspiration and support as well as the opportunity to discuss with them their ideas over the past 15 and 11 years respectively.