Cognitive Thermometers: Machine Learning and Logical Complexity

Humans effortlessly go beyond literal meanings: If you mow the lawn, I will give you fifty dollars, is typically understood as implying that the speaker will pay only if the lawn is mowed, whereas If you are hungry, there is pizza in the oven implies that pizza is available regardless of the hearers hunger. Large Language Models - LLMs - show human-like performance on many tasks, yet it remains unclear whether they reason like humans. To address this, we conducted a population-matching experiment assessing how twentyfive LLMs compute conditional inferences across four languages, compared to an equal number of humans per language. We find that humans enrich logical reasoning through pragmatic inferences across languages. Model behavior is more variable. Some LLMs perfectly follow the truth-table of conditionals but they ignore pragmatic inferences, while others deviate from the truth-table, adhering to a single interpretation across the board, thus reflecting accurate rule-based processing but not human-like reasoning. Overall, LLMs are accurate semantic operators, but fail to capture the pragmatic enrichments characteristic of human reasoning. Crucially, LLM accuracy is neither predicted nor boosted by open vs. closed status, training orientation, or architecture type, suggesting that pragmatic reasoning is still an emerging ability in the cognitive toolkit of artificial systems.

Semantic memory retrieval can be conceptualized as navigation through conceptual space. We compared semantic search dynamics between humans and three large language models (GPT-4o, Gemini-2.5-Pro, Claude-Sonnet-4.5) using verbal fluency data. By applying trajectory-based NLP metrics to the items generated by 82 human participants and LLM output across eight temperature settings, we quantified three complementary dimensions: entropy (step size predictability), distance to next (successive semantic steps), and distance to centroid (global dispersion). Humans exhibited higher entropy, larger semantic steps and broader dispersion than all LLMs, indicating more variable and exploratory search. Temperature tuning produced only partial alignments, as individual metrics matched between humans and LLMs at specific settings, but no configuration reproduced the complete human profile (in all dimensions). These findings suggest that human semantic search implements a distinctive balance between local exploitation and global exploration that current model architectures fail to reproduce.

We introduce the ladderpath index as a measure of language complexity grounded in algorithmic information theory. It counts the minimum steps needed to reconstruct a sequence through hierarchical reuse of repeated substructures, capturing an exactly computable but constrained form of algorithmic compressibility related to, but distinct from, Kolmogorov complexity. We apply the ladderpath approach to 21 parallel corpora from the Parallel Universal Dependencies dataset. The ladderpath index is approximately invariant across the languages, and varies much less than the corpus length. This is more pronounced when all corpora are mapped to a unified binary representation, providing evidence for the equi-complexity hypothesis from a representation-independent perspective. We also observe trade-offs between character inventory size and corpus length, and between vocabulary-level and corpus-level reconstruction complexity, supporting the trade-off hypothesis that total complexity is conserved and redistributed across linguistic levels. The reusable substructures identified by the ladderpath approach, without any linguistic input, overlap with words and morphological components attested in the natural vocabulary. The hierarchical reuse captured by the ladderpath approach parallels the chunking mechanisms proposed in cognitive science, where the human cognitive system compresses linguistic input into nested, reusable units under shared memory and processing constraints. This connection between cognitive chunking and the ladderpath approach provides a new interpretation for the equi-complexity and trade-off hypotheses, grounding both in the shared cognitive architecture that underlies language processing across human languages.