MCS Theory of Cognition – Definitions and Metrics for Core Concepts
Content:
Preamble
Introduction
Definitions, in alphabetical order
Particular reference
Preamble
This part of the site summarizes the most central elements of the MCS (Model for Cognitive Sciences) theory of cognition.
A first approach focused on artificial intelligence (AI) in a restricted set of core concepts in cognition, summarized here.
Then it appeared that cognition had to be revisited in a broader way, including the cultural ensemble linked to the imaginary, such as time or the question of models and definitions, of epistemology.
Finally, the angle of observation has opened up further to consider, in addition to cognition and the imaginary, the real, the values, and the collective.
Thus additional information is available in the other pages of this site and more elsewhere:
- A comprehensive presentation is available in the corresponding book(s) [1]: https://www.roboptics.ch/publications-jdd-plus/.
- Supplements and links related to cognition are further available on our corresponding classic website, currently being migrated: cognitics.populus.org/rub/3 .
[1] Jean-Daniel Dessimoz, « Cognition and Cognitics – Definitions and Metrics for Cognitive Sciences, in Humans, and for Thinking Machines, 2nd edition, augmented, with considerations of life, through the prism “real – imaginary – values – collective”, and some bubbles of wisdom for our time », Roboptics Editions llc, Cheseaux-Noreaz, Switzerland, 345 pp, March 2020.
Introduction
A cognition theory (MCS cognition theory) has been developed, which gives scientific definitions of core cognitive properties, such as knowledge or learning, with mathematical equations allowing for a quantitative assessment of those properties.This cognition theory characterizes (cognitive) systems by their input and output information flows, as well as by time features.
The core definitions of MCS cognition theory are briefly presented below, in alphabetical order. This can validly be viewed as a glossary, an ontology or an axiomatic declaration. The number behind each concept denotes the logical order in which definitions are introduced.
1 Model
2a Information 2b Message
3a Complexity 3b Abstraction 3c Concretization
4a Knowledge 4b Experience 4c Fluency 4d Simplicity
5a Expertise 5b Reductibility
6 Learning
7 Intelligence
8a Right 8b True 8c Good 8d Wrong 8e False 8f Bad, Evil
9 Wisdom
10 Sapience
Definitions, in alphabetical order
Abstraction is the property of a system that generates less information than it receives. The abstraction index, iabs, is the ratio of incoming information quantity (ni [bit]) over the outcoming information quantity (no [bit]). Inverse of concretization. Equ.: iabs=ni/no [without unit]
Bad is the the contrary of “good“. “Evil” is essentially a synonym for bad.
Complexity is the property of an object which requires a lot of information in order to be exhaustively described. Quantitatively, complexity is the amount of required information. Unit: same as for information, i.e. [bit]
Concretization is the property of a system which generates more information than it receives. The concretization index, ic, is the ratio of outcoming information quantity (no [bit]) over the incoming information quantity (ni [bit]). Inverse of abstraction. Equ.: ic=no/ni [without unit]
Experience is the property of a system that has been exposed to a cognitive domain. Quantitatively, it is usually evaluated in the form Rt, in terms of time (duration) [s]. Another approach (less intuitive) consists in evaluating the experience, Ri, in terms of the number Na of cognitive operations encountered, i.e. associations of messages in principle observed, in input and, in correspondence, in output. Equ: Ri=Na*Sum(ni,no) [bit]
(On the other hand, if one wishes, on the formal level, it remains possible to unify the two definitions proposed for the experience by characterizing the environment where it is acquired by the abundance of the cognitive operations which take place there, in bit per second).
Expertise is the property of a cognitive system which delivers fast the pertinent output information. Quantitatively, it is the product of knowledge, K, and fluency, f. Equ.: E=K*f . The unit is [lin/s]. In general terms, synonyms for expertise include know-how, skill, competence and excellence.
False is the contrary of true.
Fluency is the property of a system which delivers information fast. It can be viewed as a processing speed. Fluency, f, is the inverse of the time duration , Dt, necessary to deliver output information. Equ. : f=1/Dt [1/s]
Good can readily be defined on the basis of “right”: “Good” is “right” when the law to comply with is “to progress towards a chosen goal”. For example, if a robot is required to move, it is good for it to switch on some power circuits.
Information is what allows a receiver to update his/her/its own internal model. Information is an antidote to uncertainty. The amount of information received is the difference in size of the model in terms of information content, between the states “before” and “after” the arrival of the message. The calculation is based on the probability of the messages, which are essential elements of the model. Let us consider an incoming message, expected by the receiver as one of N possible messages, with probability p. According to Shannon’s classical theory, the quantity of information, Q, carried by this message is all the greater as it cancels out a large uncertainty, that is, it makes a probability initially judged to be very low become certain; the quantity of information carried by this message varies with the inverse of its probability; precisely, Q amounts to log (1/p). The logarithm is generally taken in base 2, which gives the unit [bit]. If the individual probability of the different messages is pi, where pi is the probability of the ith message, leading to the respective quantities of information Qi, then the average quantity of these messages, Qa, is given by the following equation: Qa:= Sum for i:= 1 to N of (pi x Qi).
(Note that the amount of information contained in a specific message depends essentially on the expectations of the receiver and this amount can therefore vary in two ways: 1. in relation to the different receivers considered and 2. in relation to the passage of time, and more particularly taking into account the messages already received previously)
Intelligence is the property of a system capable of learning. In quantitative terms, intelligence can be assessed as an index, i, which is the ratio of learning with respect to experience. Depending on the choice, intuitive or more rigorous, of the formulations introduced for experience, we have two equations. Equ.: i=L/Dt [lin/s2] (or i=L/DR [lin/s/bit]).
The first formulation is simpler and defines intelligence in a very pleasant way as a kind of acceleration, cognitive.
Knowledge is the property of a system which delivers the pertinent output information, either proactively or in response to incoming messages. Quantitatively it is given by the following equation: K=log(no*2power(ni) +1). The logarithm is in base 2, and the unit is the [lin].
Learning is the process of a system that learns, i.e. increases its level of expertise, over time (or better: as it gains experience). Over a certain period of time, the amount of learning is thus the amount of expertise acquired in addition. Equ: L=E(t1)-E(t0). Another point of view: L=E(r1)-E(r0). In both cases, the unit is the expertise, the [lin/s].
A message is a piece of information. Essentially, the amount of information a message carries is determined by its probability of occurrence.
In general terms, a model is a simplified (i.e., inherently incomplete) representation of reality that is found to be useful for achieving a specific objective, a value.
In the MCS theory of cognition, the basic reference model for a cognitive agent or system is behavioral. A cognitive domain can be schematically described as a kind of (virtual) table containing all the input-output associations, with as many rows as possible types of incoming messages, each containing the corresponding output message. There is no question of realizing cognitive systems on this rough basis. On the other hand, the useful and valid objective of this model is to allow the quantitative evaluation of key cognitive properties, such as knowledge, expertise or learning.
Reductibility is the property of a system which can be implemented by subsystems of integral complexity smaller than the complexity of the system itself.
“Right” is usually considered as a logic, Boolean value, complementary to “wrong”. Let us define “right” as the qualifier of an entity that complies with a given law (assertion). For example if the law is “to move ahead”, a step forward is “right”.
Sapience is the essential property of a cognitive agent, i.e. of an active structure capable of cognition. It appears under a number of signs, such as knowledge, expertise, or intelligence (already defined and made measurable in MCS). Quantitatively, sapience may be characterized by an index, in reference to humans (“homo sapiens”). Sapience (index) is thus a ratio; no specific unit.
Simplicity is the property of an object which requires little information in order to be exhaustively described. Quantitatively, simplicity is the inverse of complexity. Unit: inverse of information unit, [1/bit].
True can be defined on the basis of “right”: “True” is “right”, when the law to comply with is “correspondence to the real”. For example it is true that braking reduces speed.
Wisdom is a specific property of cognitive agents, which refers to their ability to take good decisions, i.e. to be expert in delivering the messages that make an agent reach a given goal.
To make it simple and easy, we propose here to estimate in Boolean terms the quantity of wisdom for an agent, on a given domain: true or false, reflecting the fact that the goal is being reached or not by the agent. Without being essential, a usual feature of wisdom is to relate to complex situations and major or “meta”-goals: to survive, to win the game, to gain a place in the Hall of Fame.
Wrong is the contrary of right.
Particular reference:
Jean-Daniel Dessimoz, « Cognition and Cognitics – Definitions and Metrics for Cognitive Sciences, in Humans, and for Thinking Machines, 2nd edition, augmented, with considerations of life, through the prism “real – imaginary – values – collective”, and some bubbles of wisdom for our time », Roboptics Editions llc, Cheseaux-Noreaz, Switzerland, 345 pp, March 2020.
Other documents, can be downloaded, in French or English versions, from the given website (www.roboptics.ch/publications-jdd-plus).