A mathematical approach to cognitive processes

Area of Science:

• Cognitive Science
• Mathematical Modeling
• Theoretical Neuroscience

Background:

• Cognitive processes lack a precise mathematical framework.
• Previous work established foundational concepts in 'Experientia'.

Purpose of the Study:

• To present a mathematical formalization of cognitive processes.
• To define cognitive processes using interaction probabilities and stability parameters.

Main Methods:

• Describing cognitive processes as exponentially decaying interaction probabilities.
• Introducing a 'cognitive string' and 'cognitive plasma' analogy.
• Defining 'cognitive stability' via an association parameter.

Main Results:

• Cognitive processes are modeled as a system of decaying interaction probabilities.
• The association parameter quantifies cognitive stability.
• Cognitive complexity is directly proportional to time.

Conclusions:

• The proposed mathematical model offers a novel perspective on cognitive dynamics.
• This formalization provides a basis for quantifying cognitive complexity and stability.
• The model suggests a time-dependent nature of cognitive process complexity.