Second-Order Systematicity of Associative Learning: A Paradox for Classical Compositionality and a Coalgebraic...

Area of Science:

• Cognitive Science
• Theoretical Computer Science
• Mathematical Psychology

Background:

• Systematicity in cognitive architecture links cognitive capacities through shared structures.
• Classical explanations rely on syntactic/symbolic structures.
• Second-order systematicity (systematic learning) is under-explored.

Purpose of the Study:

• Introduce learned associations as a form of second-order systematicity.
• Address the paradox learned associations pose for classical cognitive theories.
• Propose a category-theoretic framework to explain both first and second-order systematicity.

Main Methods:

• Utilize category theory, specifically universal morphisms, to model systematicity.
• Generalize compositionality from representations to processes.
• Derive a model of systematic associative learning using (co)recursion.

Main Results:

• Learned associations are presented as a novel instance of second-order systematicity.
• A category-theoretic explanation resolves the paradox posed by associative learning for classical theories.
• Universal morphisms provide a unified account for both first and second-order systematicity.

Conclusions:

• Category theory offers a robust foundation for understanding cognitive architecture.
• The proposed framework unifies diverse forms of systematicity.
• This work supports a category-theoretic approach to cognitive science and learning.