Categorical Syllogisms Revisited: A Review of the Logical Reasoning Abilities of LLMs for Analyzing Categorical Syllogisms
Bibliographic record
Abstract
There has been a huge number of benchmarks proposed to evaluate how large language models (LLMs) behave for logic inference tasks. However, it remains an open question how to properly evaluate this ability. In this paper, we provide a systematic overview of prior works on the logical reasoning ability of LLMs for analyzing categorical syllogisms. We first investigate all the possible variations for categorical syllogisms from a purely logical perspective and then examine the underlying configurations (i.e., mood and figure) tested by existing datasets. Our results indicate that compared to template-based synthetic datasets, crowdsourcing approaches normally sacrifice the coverage of configurations (i.e., mood and figure) of categorical syllogisms for more language variations, thus bringing challenges to fully testing LLMs under different situations. We then summarize the findings and observations for the performance of LLMs to infer the validity of syllogisms from the current literature. The error rate breakdown analyses suggest that the interpretation of quantifiers seems to be the current bottleneck that limits the performance of the LLMs and is thus worth more attention. Finally, we discuss several points that might be worth considering when researchers plan to release categorical syllogism datasets. We hope our work will provide a timely review of the current literature regarding categorical syllogisms, and motivate more interdisciplinary research between communities, specifically computational linguists and logicians.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.006 |
| Science and technology studies | 0.000 | 0.006 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".