Dual-process theories posit that separate kinds of intuitive (Type 1) and reflective (Type 2) processes contribute to reasoning. Under this view, inductive judgments are more heavily influenced by Type 1 processing, and deductive judgments are more strongly influenced by Type 2 processing. Alternatively, single-process theories propose that both types of judgments are based on a common form of assessment. The competing accounts were respectively instantiated as two-dimensional and one-dimensional signal detection models, and their predictions were tested against specifically targeted novel data using signed difference analysis. In two experiments, participants evaluated valid and invalid arguments, under induction or deduction instructions. Arguments varied in believability and type of conditional argument structure. Additionally, we used logic training to strengthen Type 2 processing in deduction (Experiments 1 & 2) and belief training to strengthen Type 1 processing in induction (Experiment 2). The logic training successfully improved validity-discrimination, and differential effects on induction and deduction judgments were evident in Experiment 2. While such effects are consistent with popular dual-process accounts, crucially, a one-dimensional model successfully accounted for the results. We also demonstrate that the one-dimensional model is psychologically interpretable, with the model parameters varying sensibly across conditions. We argue that single-process accounts have been prematurely discounted, and formal modeling approaches are important for theoretical progress in the reasoning field.