Shared Protentions in Multi-Agent Active Inference.

Area of Science:

• Interdisciplinary research combining phenomenology, theoretical biology (active inference), and mathematics (category theory).
• Focus on theoretical frameworks for understanding social action and collective behavior.

Background:

• Husserlian phenomenology offers insights into inner time-consciousness (retention, primal impression, protention).
• Active inference provides a formal framework for agent behavior modeling using variational Bayesian inference.
• Category theory, specifically sheaf and topos theory, offers advanced mathematical tools for modeling complex systems.

Purpose of the Study:

• To develop a comprehensive framework for understanding social action based on shared goals.
• To formalize shared goals using shared protentions and explore the emergence of group intentionality.
• To mathematically model individual and group interactions within stochastic environments.

Main Methods:

• Overview of Husserlian phenomenology and active inference principles.
• Integration of shared protentions with active inference's shared generative models.
• Application of sheaf and topos theory for mathematical representation of agent interactions and worldviews.
• Utilizing morphisms between polynomial representations of agent models.

Main Results:

• A unified framework linking phenomenology, active inference, and category theory for social action.
• Formalization of shared goals in terms of shared protentions, illuminating group intentionality.
• Mathematical modeling of agent interactions and consensus using sheaf and topos theory.
• Identification of shared protentions as crucial for coordination and achieving common objectives.

Conclusions:

• The integrated framework provides a novel approach to understanding collective goal-directed behavior.
• Shared protentions are key emergent properties facilitating group coordination.
• Acknowledges challenges posed by stochasticity and uncertainty in achieving shared goals.