**MCS Cognition Theory**

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

9 Wisdom

10 Sapience

Abstraction (3b)

Abstraction is the property of a system which 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 (8f)

Bad is the the contrary of "good".

**Complexity (3a)**

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 (3c)

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(4b)

Experience is the property of a system which has been exposed to a cognitive domain. Quantitatively, it is usually evaluated in terms of time (duration) [s]. An alternate (better?) view is to assess experience, R, in terms of number Na of witnessed input-output message associations. Equ.: R=Na*Sum(ni,no) [bit]

**Expertise (5a)**

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 (8e)

False is the contrary of true.

Fluency(4c)

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 (8c)

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 (2a)

Information is what allows a receiver to update his/her/its own internal model. Quantitatively, it is the difference of model size in terms of information content, between the states “before” and “after” message arrival. Computation is made on the basis of message probabilities, which are essential elements in the model. Consider that the incoming message is expected by the receiver to be one among N possible variants. If the probabilities of those various occurrences of the message are pi, where pi is the probability of the ith message, then the average quantity Qa is given by the following equation: Qa:= Sum for i:= 1 to N of (pi log 1/pi ). The log is usually taken in base 2, thereby yielding [bit].

(notice that the quantity of information contained in a specific message essentially depends on *receiver's* expectations and thus may vary 1. with respect to considered receivers and 2. in time)

**Intelligence (7)**

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 intuitive or more rigorous choice of formulations introduced for experience, we have two equations. Equ.: i=L/Dt [lin/s2] (or i=L/DR [lin/s/bit])

**Knowledge (4a)**

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 log is in base 2, and the unit is the [lin].

Learning (6)

Learning is the property of a system capable of increasing its expertise level as time goes (or better: as experience goes). Equ: L=E(t1)-E(t0). Alternate view: L=E(r1)-E(r0). In both cases the unit is [lin/s].

Message (2b)

Messages essentially consist in pieces of information. Quantitatively, they are fundamentally characterized by their probability of occurence.

Model (1)

In general terms, a model is a simplified (that is, incomplete by essence) representation of reality, which is found useful in order to reach some specific goal. In MCS the basic reference model is behavioral. It can be viewed as a kind of (virtual) table, which contains as many states as possible incoming message types; each state contains the instant probability of occurrence for the corresponding input message, and also contains the corresponding output message. The goal of this model is to allow the quantitative assessment of key cognitive properties, such as knowledge, expertise, or learning.

Reductibility (5b)

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 (8a)

“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 (10)

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 (4d)

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 (8b)

True can be defined on the basis of “right”: “True” is “right”, when the law to comply with is “correspondence to reality”. For example it is true that braking reduces speed.

Wisdom (9)

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 (8d)

Wrong is the contrary of right.