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A Systematic Comparison of Syllogistic Reasoning in Humans and Language Models
Tiwalayo Eisape, MH Tessler, Ishita Dasgupta, Fei Sha, Sjoerd van Steenkiste, Tal Linzen
TL;DR
The paper asks whether language models trained on human-generated text reason more logically than humans and whether their biases resemble human biases. It compares PaLM 2 syllogistic reasoning with human performance, finding better accuracy alongside systematic errors that partly mirror human reasoning.
Problem
The paper asks whether language models reason more logically than humans and whether their deviations from logic resemble human biases.
Source: §1 · p. 1Method
The paper examines PaLM 2 models’ syllogistic reasoning and compares their errors with human reasoning patterns.
Source: §7 · p. 9Results
Takeaways & Limitations
The findings show that language models can reproduce human reasoning biases while overcoming some of them, though their overall reasoning remains short of perfect logical reasoning.
Source: §1 · p. 2The interpretation uses Mental Models Theory, but other accounts of human reasoning may apply, and language models may fit none of them.
Source: Ethical Considerations and Limitations · p. 10
Abstract
from arXiv · showhide
A central component of rational behavior is logical inference: the process of determining which conclusions follow from a set of premises. Psychologists have documented several ways in which humans' inferences deviate from the rules of logic. Do language models, which are trained on text generated by humans, replicate such human biases, or are they able to overcome them? Focusing on the case of syllogisms -- inferences from two simple premises -- we show that, within the PaLM2 family of transformer language models, larger models are more logical than smaller ones, and also more logical than humans. At the same time, even the largest models make systematic errors, some of which mirror human reasoning biases: they show sensitivity to the (irrelevant) ordering of the variables in the syllogism, and draw confident but incorrect inferences from particular syllogisms (syllogistic fallacies). Overall, we find that language models often mimic the human biases included in their training data, but are able to overcome them in some cases.
1 Introduction
The paper asks whether language models can reason more logically than humans despite training on human-generated text, and whether their biases resemble human biases. Comparing PaLM 2 models with human syllogistic reasoning, it finds greater accuracy alongside systematic errors that sometimes mirror human reasoning.
1 Introduction
- PaLM 2 models draw correct inferences more often than humans, but even the best reaches only about 75% accuracy and scale does not consistently improve accuracy.Larger models tend to be more accurate than smaller ones.Source: §1 · p. 2
- Models struggle with some syllogisms that humans also find difficult, yet larger models correctly solve some syllogisms that are difficult for humans.The models’ errors overlap with human errors only partly.Source: §1 · p. 2
- Like humans, language models show an irrelevant variable-ordering effect and make high-confidence, low-accuracy syllogistic fallacies.Larger models are somewhat more susceptible to these fallacies than smaller ones.Source: §1 · p. 2
- The paper uses Mental Models theory to find quantitative evidence that larger language models reason more deliberatively than smaller ones.Source: §1 · p. 2
2 Background and Related Work
Syllogisms combine two premises about three terms to test whether a relationship between the unshared terms follows. Prior work documents systematic human reasoning biases and proposes mental models as one account; this paper studies language-model deduction in a controlled task and extends earlier analyses of syllogisms.
2.1 Syllogisms
- Four quantifiers and four pairs of variable orderings combine to form 64 syllogism types; 27 entail an A–C relationship, while 37 license no such relation.Source: §2.1 · p. 2
2.2 Human Syllogistic Reasoning
- Human syllogistic errors are systematic: difficulty varies by syllogism, and premise ordering can bias conclusion ordering even though it does not change logical validity.Participants may also favor conclusions that are true in the real world, regardless of whether the premises entail them.Source: §2.2 · pp. 2–3
- Mental Models Theory proposes that reasoners construct small worlds instantiating the premises, with fallible heuristics accounting for errors.Source: §2.2 · p. 3
2.3 Language Models and Reasoning
- This study targets deduction based only on premises in a controlled task with extensive human data, extending prior syllogism work beyond content effects.Earlier controlled work examined formal logic without comparing results to humans; a close study demonstrated content effects in syllogisms.Source: §2.3 · p. 3
3 Methods
The study uses human syllogism responses and content-neutralized stimuli, then evaluates pretrained language models with zero-shot chain-of-thought prompting and sampled responses. Its figures organize model, human, and oracle accuracy and response-pattern comparisons across syllogisms.
3.1 Data
- Human responses come from 139 participants who each answered every syllogism once; the study also uses 30 content triples without obvious semantic associations, yielding 1,920 data points.Source: §3.1 · pp. 3–4
- Figure 2 displays PaLM 2, human, and random-guessing accuracy by syllogism, grouping syllogisms by variable ordering and ranking them by human accuracy.The figure’s inset gives average accuracy across syllogisms; the random baseline varies because some syllogisms have multiple valid conclusions.Source: Figure 2 · p. 4
3.2 Models and Inference
- The study primarily evaluates four PaLM 2 sizes and also examines Llama 2 models, whose results are preliminary because evaluation hyperparameters were not explored.Models receive zero-shot chain-of-thought prompts, with conclusions randomized to control for answer-order sensitivity.Source: §3.2 · p. 4
- For each reasoning problem, the researchers estimate conclusion probabilities from 30 sampled proposals, reject responses without an exact conclusion match, and select the highest-probability conclusion.Figure 3 compares model and human response distributions with a logically correct oracle; Figure 4 compares A–C and C–A conclusion probabilities and the magnitude of the ordering effect.Source: §3.2 · pp. 4–5, Figure 3 · p. 4, Figure 4 · p. 5
4 Results1
PaLM 2 accuracy generally improves with scale and can exceed human accuracy, while its errors still show human-like patterns. Llama 2 has similar aggregate accuracy to humans but a different profile across syllogisms.
4.1 Do LMs Reason Accurately?
- PaLM 2 accuracy generally rises with scale, and the two largest models exceed human accuracy, though the largest trails the second-largest and some syllogisms worsen with scale.Accuracy varies substantially by syllogism, and some remain difficult across all model sizes.Source: §4.1 · p. 5
4.2 Do LMs Reason Like Humans?
- PaLM 2’s difficult syllogisms overlap with humans’, yet larger models solve some human-difficult cases; response distributions correlate highly with humans, including for more-accurate models.Human accuracy averages roughly 50% across syllogisms; response-distribution correlation is highest for PaLM 2 Small.Source: §4.2 · p. 5
- All PaLM 2 models show the same variable-ordering effect as humans, with a somewhat larger bias and no clear increase as model size grows.The premise ordering is logically irrelevant, but models favor conclusions whose variable ordering follows the premise ordering.Source: §4.2 · p. 6
- The top three human syllogistic fallacies are also outliers for PaLM 2, and larger models’ accuracy–entropy residuals correlate more strongly with humans’ (Figure 5).These fallacies pair low accuracy with low response entropy, indicating confident, consistent errors.Source: §4.2 · p. 6, Figure 5 · p. 6
4.3 Llama 2 Results
- Llama 2’s aggregate accuracy is similar to humans’ and rises modestly with scale, but it struggles on some syllogisms humans find easy while showing a human-like ordering effect.Unlike PaLM 2, Llama 2 struggles with some A-type syllogisms that humans find easy.Source: §4.3 · p. 7
5 Interpreting Language Models Using Mental Models Theory
The paper interprets syllogistic behavior through mReasoner, a mental-model account that constructs premise-consistent entities and can search for counterexamples. Its simulations and principal-component analysis identify a deliberative-reasoning dimension that is more prominent in larger PaLM 2 models, including when accuracy is controlled away.
5 Interpreting Language Models Using Mental Models Theory
- mReasoner represents premises with mental models of entities and may revise an initial conclusion after searching for a counterexample.In the illustrated case, splitting an entity produces a counterexample and the reasoner updates to “nothing follows.”Source: §5 · pp. 7–8
- Four hyperparameters govern mReasoner’s model construction and revision: LEN, BROAD, SYSTM2, and WEAKEN.SYSTM2 controls counterexample search; WEAKEN controls whether a response is weakened or changed to “nothing follows” after a counterexample.Source: §5 · pp. 7–8
- The analysis represents 923 completed mReasoner simulations in a 216-dimensional behavior space and uses PCA to identify its top four components.The simulations sampled 1,296 parameter settings; 923 finished before timing out.Source: §5 · p. 8
- The first principal component captures 77% of mReasoner behavioral variance and loads most on SYSTM2, while the second loads on BROAD but explains less variance.Figure 8 relates the components to mReasoner’s parameters and accuracy.Source: §5 · p. 8, Figure 8 · p. 8
- Larger PaLM 2 models show a stronger deliberative-reasoning signature, which remains when correct-answer probabilities are zeroed and is then correlated 0.6 with SYSTM2.In that control, the deliberative component has zero correlation with accuracy, and correlations with other parameters are below 0.15.Source: §5 · pp. 8–9, Figure 9 · p. 8
6 Discussion
The discussion weighs accuracy against human-likeness, uses cognitive-science findings to interpret model behavior, and reports only partial support for the idea that language models replicate human biases.
6 Discussion
- The authors prioritize accuracy for most applications, while identifying cognitive modeling as an exception where human-like reasoning is the goal.They describe cognitively informed model development as a future direction.Source: §6 · p. 9
- Larger models are slightly more correlated with human responses in some cases, but models also overcome human biases on some syllogisms.The authors suggest source code in PaLM 2 training data as one possible explanation and propose testing training-corpus composition in future work.Source: §6 · p. 9
- Cognitive-science biases serve as hypotheses for model behavior, with partial support from cases where larger models are more calibrated to human responses.This calibration pattern is particularly noted in the analysis of the correlation between accuracy and entropy.Source: §6 · p. 9
- Under the assumption that language models use human-like heuristic strategies, Mental Models Theory suggests that larger models reason more deliberatively.The paper uses a computational cognitive model developed to explain human reasoning to interpret model behavior.Source: §6 · p. 9
7 Conclusion
The conclusion reports that the largest PaLM 2 models make fewer mistakes than humans on syllogisms, while retaining systematic errors and qualitative biases that only partly align with human errors.
7 Conclusion
- The largest PaLM 2 models make significantly fewer mistakes than humans, but still display systematic errors.The conclusion situates this comparison within syllogistic reasoning.Source: §7 · p. 9
- Language-model errors are only partly aligned with human errors, and models remain susceptible to several qualitative reasoning biases shown by humans.Source: §7 · p. 9
- The paper examines whether self-supervised learning can yield correct reasoning despite human-produced training data and human deviations from normative logic.Source: §7 · p. 9
Ethical Considerations and Limitations
The authors hope the work will inform cognitively informed and ethical model development, while noting limits in comparing human and model behavior, evaluating elicitation approaches, and interpreting reasoning through one cognitive theory.
Ethical Considerations and Limitations
- Directly comparing language-model and human behavior presents challenges.The paper flags these as a limitation on interpreting the comparisons.Source: Ethical Considerations and Limitations · pp. 9–10
- The authors hope the work will facilitate cognitively informed and ethical model development.Source: Ethical Considerations and Limitations · p. 9
- The evaluation focuses on zero-shot chain-of-thought, while a systematic comparison of elicitation approaches remains future work.Other discussed options include model generation, meta-level judgments, continuation probabilities, few-shot evaluation, and varied prompts with or without chain-of-thought.Source: Ethical Considerations and Limitations · p. 10
- Mental Models Theory is one possible account of language-model reasoning, and systematic comparison with alternative theories is left for future work.The alternatives discussed include normative logic, constrained probabilistic inference, and combined probabilistic, heuristic, and pragmatic reasoning.Source: Ethical Considerations and Limitations · p. 10
A Further Details on Syllogism Dataset
The experiments use content triples whose words were chosen to minimize semantic associations with one another.
A Further Details on Syllogism Dataset
- The experimental dataset uses content triples, with words selected to have minimal semantic associations with each other.Table 2 lists the triples used in the experiments.Source: A Further Details on Syllogism Dataset · p. 12
B Prompting and Evaluation
The appendix compares generative chain-of-thought prompting with multiple-choice and binary discrimination methods for eliciting syllogistic inferences. Chain-of-thought performs best overall, while binary discrimination is better at identifying cases where nothing follows.
B Prompting and Evaluation
- Chain-of-thought prompting has the highest accuracy generally, while binary discrimination better elicits “nothing follows” and has the highest correlation with humans.Multiple-choice performs substantially worse than both methods.Source: B Prompting and Evaluation · pp. 12–13, Figure 13 · p. 15
- The evaluation uses 30 content-word triples chosen to be minimally semantically associated, substituting each triple for the syllogism’s three variables.Table 2 identifies the triples used.Source: Table 2 · p. 13
- The appendix reports that all its empirical results use PaLM 2 models.The main text uses generative chain-of-thought prompting after comparing the three elicitation strategies.Source: B Prompting and Evaluation · pp. 12–13
B.1 Generative Evaluation with a Zero-Shot Chain-of-Thought Prompt
- The generative method prompts the model to reason step by step, then selects the conclusion most often detected across content triples and samples.The conclusion list is randomized and includes “nothing follows.”Source: §B.1 · p. 13
B.2 Multiple-Choice Discriminative Evaluation
- Multiple-choice scoring uses mutual information between the prompt and each possible conclusion, then normalizes scores into a distribution and selects the highest-scoring conclusion.The nine options comprise eight valid conclusions and “nothing follows.”Source: §B.2 · p. 14
B.3 Simplified Binary Evaluation
- Binary discrimination scores each of eight candidate conclusions as valid or invalid using mutual information, then normalizes validity probabilities across conclusions.This approach omits “nothing follows” as an individual candidate.Source: §B.3 · p. 16
- Binary discrimination predicts “nothing follows” when no candidate conclusion exceeds 50% probability of being valid.The paper reports it as the only method that successfully elicits “nothing follows” for a substantial proportion of syllogisms.Source: §B.3 · p. 16
B.1.1 Robustness to Prompt and Decoding Hyperparameters
The appendix checks prompt and decoding choices for robustness, reporting broadly similar patterns across prompt variants and a slight accuracy increase with longer decoding. It also includes supplementary human-correlation and mReasoner analyses.
B.1.1 Robustness to Prompt and Decoding Hyperparameters
- The main analyses generate 75 tokens at temperature 0.5 and use 30 samples per syllogism-type and content-triple combination.Because of compute limits, hyperparameter variations are explored only for PaLM 2 XS and accuracy is reported only on the 27 syllogisms with valid conclusions.Source: §B.1.1 · p. 13
- Three prompt variants replace or omit the reasoning trigger, or emphasize “nothing follows” more prominently; Figure 11 shows the variations.The variants are logically, empty, and alt.Source: §B.1.1 · p. 13, Figure 11 · p. 14
- Prompt variants show broadly similar accuracy patterns, with stepxstep moderately more accurate than the alternatives.These comparisons hold temperature at 0.5 and the token limit at 75.Source: §B.1.1 · p. 14
- Accuracy increases slightly as decoding length rises from 50 to 100 tokens, while temperature is separately varied across 0.25, 0.5, and 0.75.The prompt is held at stepxstep; Figure 12 presents the variations.Source: §B.1.1 · p. 14
C By-Syllogism Correlations with Human Responses
- Larger models are generally more human-like in syllogism-level correlations, but the relationship varies and IE2 becomes less correlated as models grow.Figure 14 presents the by-syllogism correlations.Source: C By-Syllogism Correlations with Human… · p. 16
D.1 Model details
- The mReasoner appendix illustrates canonical sets, which depend on premise moods, and the ADD, BREAK, and MOVE routines for revising mental models.The routines respectively add an entity, decompose an entity into property subsets, or move a property between entities.Source: §D.1 · p. 16
D.2 mReasoner instantiations
- The authors instantiate 1,296 mReasoner models from a parameter grid, retaining 923 after excluding models that failed to complete 100 trials within 60 seconds.Each retained model is represented by a 216-dimensional response vector, and the authors apply PCA to those vectors.Source: Table 3 · p. 16, §D.2 · p. 16
E Llama 2: Additional Results and Plots
Llama 2’s aggregate accuracy resembles humans’, but its errors differ substantially from human patterns and its behavior is less correlated with humans than PaLM 2’s. Its apparent increase in deliberative reasoning with scale disappears when accuracy is controlled.
E Llama 2: Additional Results and Plots
- Despite human-like aggregate accuracy, Llama 2 models have lower human-response correlations than PaLM 2, with poor accuracy on some human-easy syllogisms and high accuracy on some human-difficult ones.The accuracy-and-entropy analysis also shows a slight decrease in human correlation with increasing model size.Source: E Llama 2: Additional Results and Plots · p. 16, Figure 19 · p. 19, Figure 21 · p. 20
- Llama 2 shows increased signatures of deliberative reasoning with model size when all predictions are included, but not after controlling for accuracy.The control sets correct-answer probabilities to zero before projecting behavior into mReasoner’s principal-component space.Source: E Llama 2: Additional Results and Plots · p. 18, Figure 17 · p. 19
- Figure 18 partitions Llama 2 and human accuracy by variable ordering and syllogism, with random-guessing accuracy varying by syllogism.Figure 19 plots accuracy against entropy and relates Llama 2 fallacy residuals to human residuals.Source: Figure 18 · p. 19, Figure 19 · p. 19
- Llama 2 and humans show variable-ordering effects in the same direction, despite the ordering’s logical irrelevance.Figure 20 compares marginal conclusion probabilities and the magnitude of the ordering effect.Source: Figure 20 · p. 20