Developing BOLT – A Matrix Test Using Boolean Operations to Assess Logical Thinking

Matrix reasoning tasks are widely used measures of fluid reasoning. Despite variation in construction principles, four difficulty components recur across tests: the number of elements, the number of rules, rule type, and perceptual organization. Among these, rule type is particularly central and can be formally classified into unary, binary, and ternary operations. Accordingly, we introduce BOLT (Boolean Operations and Logical Thinking), a matrix test grounded in Boolean algebra as the formal framework for item generation. Across two online pilot studies (Study 1: N = 473, 45 items; Study 2: N = 430, 42 items) and one operational administration (Study 3: N = 7,150, 39 items), we estimated Rasch item difficulties and examined feature-based explanations of these estimates. Study 1 confirmed that the numberof binary rules was the primary driver of difficulty, whereas unary and ternary rules showed no consistent effects. For Studies 2–3, we combined cross-validated LASSO feature selection with linear logistic test models (LLTMs) to quantify contributions of structural features (number of elements, number of rules, rule types) and perceptual-organizational indices that were extracted from stimulus files. Item difficulty could be predicted with sufficient accuracy (LLTM R² = .75 in Study 2; R² = .57 in Study 3). Overall, binary operations and perceptual organization emerged as converging determinants of item difficulty in BOLT items. Future work should replicate and extend the finding that image-derived computer-vision indices make an incremental contribution beyond rule-based predictors and integrate these indices into models of matrix-item difficulty.