Cognitive Architecture as Relational Operations: A Database-Theoretic Reformulation of the Cognitive Action Model

We propose a database-theoretic reformulation of the Cognitive Action Model (CAM) that grounds personality differences in relational operations over two fundamental information structures: a Grand Premise table storing general rules, beliefs, and policies, and a Small Premise table storing current situational states and observations. This computational-level model treats action as the materialized product of JOIN operations between these tables, with vector formation occurring when stable query results satisfy both structural and regime-based constraints. Individual differences emerge from three architectural parameters that determine how information is organized, accessed, and combined. First, **lead table priority** determines whether Small Premise (extraversion) or Grand Premise (introversion) serves as the driving table in JOIN operations. This architectural choice has profound consequences: it determines cardinality constraints (one-to-many mappings), automatically strengthens specific integrity types through primary key enforcement, and produces characteristic behavioral phenotypes of flexibility versus consistency. Second, **indexing strategy** determines whether cognitive representations are organized by entities (Sensing/Feeling functions) or attributes (Intuition/Thinking functions), corresponding precisely to the database distinction between Entity Integrity (primary key preservation) and Referential Integrity (logical consistency across relationships). Third, **transaction regime** determines whether representations are treated as closure-ready (Static) or revision-tolerant (Morphing), affecting when query results can be materialized into executable action vectors. The lead table mechanism resolves a previously puzzling asymmetry in type phenomenology. All extraverts, regardless of their auxiliary function's indexing type, universally exhibit strong entity-handling capacity in immediate, concrete situations—the "here-and-now" effectiveness that characterizes extraversion. Conversely, all introverts, regardless of their auxiliary function's indexing type, universally exhibit principle-consistency across varying contexts—the stable rule-adherence that characterizes introversion. Traditional type theory notes these patterns but cannot explain them mechanistically. Our model reveals that these universal characteristics emerge not from the inherent properties of dominant functions but from their structural position: lead table status automatically strengthens entity integrity through primary key enforcement (for Small Premise leads) or referential integrity through cross-situational application (for Grand Premise leads). We demonstrate that this framework provides mechanistic explanations for multiple phenomena that resist explanation in traditional type theory: the computational basis of belief-desire action production, the extravert "flexibility" versus introvert "rigidity" phenomenology, why certain function pairs (SF and NT) integrate smoothly while others (NF and ST) require effortful translation, why cross-indexed architectures report higher cognitive overhead, and how regime preferences (J/P) create characteristic stress patterns and closure behaviors. The model generates specific, falsifiable predictions about entity-tracking performance, principle-consistency across contexts, cognitive load in dual-task paradigms, response variability under identical conditions, and learning trajectories for integrative tasks. Critically, the model is stated at Marr's computational level—specifying what cognition must accomplish and why—without claiming direct neural implementation, though we identify promising directions for future neurological grounding.