A Qualitative Model for Reasoning about Path and Support

Games offer a compelling paradigm for developing general reasoning capabilities in language models, as they naturally demand strategic planning, probabilistic inference, and adaptive decision-making. However, existing self-play approaches rely solely on terminal game outcomes, providing no mechanism to distinguish transferable reasoning patterns from game-specific heuristics. We present STRATAGEM, which addresses two fundamental barriers to reasoning transfer: domain specificity, where learned patterns remain anchored in game semantics, and contextual stasis, where static game contexts fail to cultivate progressive reasoning. STRATAGEM selectively reinforces trajectories exhibiting abstract, domain-agnostic reasoning through a Reasoning Transferability Coefficient, while incentivizing adaptive reasoning development via a Reasoning Evolution Reward. Experiments across mathematical reasoning, general reasoning, and code generation benchmarks demonstrate substantial improvements, with particularly strong gains on competition-level mathematics where multi-step reasoning is critical. Ablation studies and human evaluation confirm that both components contribute to transferable reasoning.

We introduce an extensive qualitative spatial and temporal reasoning (QSTR) benchmark for evaluating large language models (LLMs). We pose questions concerning compositional reasoning (using composition tables, CT), converse relations, and conceptual neighbourhoods (CN) for QSTR calculi, Point Algebra (PA), Allen's Interval Algebra, Interval and Duration (INDU), Region Connection Calculus (RCC-5, RCC-8, and RCC-22), the nine intersection model, cardinal direction calculus, and STAR. The RCC-22 CN is published here for the first time. An extended benchmark systematically varies question presentation including prefix/infix, words/symbols/nonce terms and schematic descriptions for selected calculi. We report results for contemporary frontier models. All models tested perform better than guessing but none can consistently answer all questions correctly. Performance varies sharply by calculus, with PA being the most straightforward, and RCC-22 the most difficult. We release the benchmark, and our results under an open licence to facilitate further assessment of qualitative spatio/temporal reasoning in LLMs.

LLM-based game agents often perform poorly on more complex tasks. This work examines whether these failures are linked to limited spatial reasoning and evaluates whether causal prompt augmentation and multi-step planning can improve win-rates while managing response latency. Using the open-source Qwen3 model family, we conduct experiments across varying model scales, reasoning modes, and planning horizons. We further introduce a focused GVGAI benchmark consisting of three custom games with five difficulty levels to isolate spatial navigation. The evaluation follows two paradigms: an initial ``positioning experiment'' to test an agent's ability to find its exact coordinates, and a study of game-play success. Our results show that while larger models with an enabled thinking mode identify their positions more accurately, overall performance in coordinate matching remains limited for smaller models. Win rates decrease as game levels and layout complexity increase, validating the benchmark's difficulty scaling. Integrating causal context into the prompts tends to improve the agents' success rates, particularly for bigger models. While enabling thinking mode and longer planning horizons significantly improve performance, multi-step planning further reduces mean per-step response times, offering a practical trade-off between reasoning depth and execution speed.