On the Co-measurability of Experimental Propositions: A Team-based Quantum Logical Analysis

In this paper, we provide a logic to reason about the compatibility structure and contextuality of quantum measurements, using inputs from the Foulis-Randall approach to operational quantum logic and the framework of team semantics. A central feature of quantum systems is that not all physical properties can be observed simultaneously. Thus, we formalize the notion of ‘co-measurability’, which captures exactly when two experimental propositions can be confirmed or refuted by a single measurement setup. We introduce the ‘Logic of Co-measurable Experimental Propositions’ ( \(L_{\mathrm C}\) $L_{\mathrm{C}}$ ), which models experimental programs as teams of measurement outcomes. Within this framework, we construct a fragment \(L_{\mathrm C}^*\) $L_{\mathrm{C}}^{\ast }$ where the conjunction of two propositions is defined to hold only if they are co-measurable. We show that this restriction naturally recovers the algebraic structure of standard quantum logic. It entails the failure of the distributive laws, which is a key feature of quantum logic. The resulting framework unifies classical and quantum scenarios, offering a logical tool for analyzing contextuality in generalized experimental settings.