Dimensional Logic as a Formal Inference System

Classical predicate logic operates under the assumption of dimensional homogeneity: statements are evaluated as either true or false, regardless of their epistemic context or the cognitive level at which they operate. This article develops a systematic extension of symbolic logic that removes this limitation. Dimensional logic introduces explicit epistemic dimensions into formal syntax, relativizes the truth predicate to multidimensional profiles, and establishes transition rules between different levels of knowledge. The resulting system retains the advantages of classical logic within the systematic dimension, while formally integrating immediate perception, reflexive metacognition, and contextual embedding. We use detailed examples (prisoner's dilemma with concrete parameters, ethical decisions, scientific statements) to show that this extended system can formally distinguish categorically different modes of validity and thus make category errors detectable as formal violations.