Contextual Probability and Operational Minimality in Tug-of-War Decision Making

Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements. The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability. Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form. The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.

Tsetlin Machines (TMs) learn interpretable Boolean clauses using finite-state automata. We introduce the Quantum-Logic Tsetlin Machine (QL-TM), which replaces Boolean literals with quantum propositions represented by projectors while retaining classical include/exclude automata. Clauses are restricted to commuting measurement contexts and activate through the Born probability of their joint projector. We prove an exact reduction to ordinary Boolean TM clauses in diagonal computational-basis contexts and connect Pauli-projector clauses to stabilizer and syndrome semantics. Controlled experiments on Bell states, phase-flip syndromes, randomized 16-class stabilizer tasks, mixed literal pools, context-budget ablations, and finite-shot noise show that correct non-diagonal contexts recover physically meaningful clauses, while diagonal or wrong contexts lose the relevant phase/syndrome information. The context-budget results closely follow the predicted separability ladder 2^(b-k) as true stabilizer generators are removed. The contribution is a controlled bridge between Tsetlin clause learning and quantum logic, not a claim of quantum advantage.

Contextual decision making uses observed covariates to guide decisions under uncertainty. Two natural approaches are predict-then-optimize (PtO), which learns the conditional expected objective, and generate-then-optimize (GtO), which learns conditional uncertainty and optimizes using generated scenarios. We study when each approach is preferable by examining how the choice of learning target affects statistical accuracy and optimization tractability. Although PtO learns a narrower target, our regret bounds show how differences in smoothness can offset GtO's additional dimensional burden. Exploiting smoothness also raises an optimization tradeoff: within the class of nonnegative-weight PtO methods studied, a lower bound limits the gains from additional smoothness, while more flexible methods may introduce signed weights and lose the guarantee of preserving convexity. GtO preserves scenario-wise convexity, but requires learning a richer object and generating scenarios for optimization. Synthetic experiments and a real case study illustrate how these tradeoffs vary with data availability and problem structure. Together with the scope for reusing a model across tasks, our findings provide practical guidance for choosing between the approaches without identifying a universal winner.