Coordination Logic: Modeling Dual Description Without Causal Assumptions

This paper introduces Coordination Logic, a formal system designed to model lawful co-variation between domains of description without presupposing causal dependence. The logic is motivated by situations where distinct vocabularies (e.g., physiological and experiential descriptions, or clinical symptoms and behavioural reports) converge on the same underlying event, but where interpreting the relation in causal terms would be inappropriate or misleading. To capture these cases, we define a new conditional operator (⇒c), interpreted as conditional coordination. Unlike material implication, ⇒c is non-vacuous, symmetric and field-dependent: it holds only when both relata are instantiated and coordinated. Semantics is three-valued, with truth tables incorporating a coordination predicate C(p,q) that determines lawful pairing. We further define a biconditional (↔c), establish its properties and develop a sequent calculus for the system. Coordination Logic departs from classical reasoning in rejecting Modus Ponens and Explosion for ⇒c, thereby preserving the non-reductive character of coordination. Applications include the formalization of non-causal dependencies in philosophy of mind, epistemology of science, psychology and psychiatry, where mistaken causal attributions are common. Our framework provides a rigorous alternative to causal or reductive logics, enriching the landscape of non-classical logics with a system grounded in dual-aspect description.