Logic

## Abstract This paper introduces a general recursive logic framework formalized through the equation $$ L_{n+1} = \sum_{i=1}^{k}(X_{i,n}Y_{i,n}), $$ and its higher-order extension $$ L_{n+1} = \sum_{i=1}^{k}(X_{i,n}Y_{i,n})^{2^n}. $$ The model is proposed as a formal mechanism for describing iterative inferential processes in logical systems. Rather than treating logical inference as a static relation between premises and conclusions, this framework conceptualizes reasoning as a recursive accumulation of structured pairwise interactions between informational components. The paper situates this model within the broader context of recursive function theory, dynamic epistemic logic, and the philosophy of formal systems. It argues that recursive aggregation provides a mathematically tractable and conceptually illuminating representation of how logical relations evolve over successive inferential stages.