Counter-arguments (CAs) are a good means to improve the critical-thinking skills of learners, especially given that one has to thoroughly consider the logic of initial arguments (IA) when composing their CA. Although several tasks have been created for identifying the logical structure of CAs, no prior work has focused on capturing multiple interpretations of logical structures due to their complexity. In this work, we create CALSA+, a dataset consisting of 134 CAs annotated with 13 logical predicate questions. CALSA+ contains 1,742 instances annotated by 3 expert annotators (5,226 total annotations) with good agreement (Krippendorff 𝛼=0.46). Using CALSA+, we train a model with Reinforcement Learning with Verifiable Rewards (RLVR) to identify multiple logical interpretations and show that models trained with RLVR can perform on par with much bigger proprietary models. Our work is the first to attempt to annotate all the interpretations of logical structure on top of CAs. We publicly release our dataset to facilitate research in CA logical structure identification.

We present FOCUS, a benchmark and task setting for Socratic question generation that delivers more informative and targeted feedback to learners. Unlike prior datasets, which rely on broad typologies and lack grounding in the source text, FOCUS introduces a new formulation: each Socratic question is paired with a fine-grained, 11-type typology and an explicit source span from the argument it targets. This design supports clearer, more actionable feedback and facilitates interpretable model evaluation. FOCUS includes 440 annotated instances with moderate partial-match agreement, establishing it as a reliable benchmark. Baseline experiments with representative state-of-the-art models reveal, through detailed error analysis, that even strong models struggle with span selection and context-sensitive categories. An extension study on the LogicClimate dataset further confirms the generalizability of the task and annotation framework. FOCUS sets a new standard for pedagogically grounded and informative Socratic question generation.