Logical Computational Linguistics

Dependency length minimization (DLM) is a well-documented processing universal, but previous studies report a single mean dependency distance (MDD) per language, obscuring variation across syntactic relation types. We analyze 122 languages in UD and SUD (version 2.17), showing that DLM operates on two distinct levels. Grammar-driven optimization targets functional dependencies (det, case, aux), which are universally short (mean 1.71, $σ$ = 0.33) and invariant across typologically diverse languages. Processing-driven optimization operates on lexical dependencies (nsubj, obj, obl), which are longer (mean 2.87), highly variable ($σ$ = 0.63), and constrained by word-order typology. This asymmetry holds in SUD despite reversed head direction (r = 0.92). We conclude that ''the grammar does the work'' of minimization by scaffolding sentences with local functional attachments, leaving processing pressures to determine the ordering of lexical heads.

Reliable confidence -- the probability that a model's own answer is correct -- is essential for the trustworthy deployment of language models. Existing work has largely evaluated confidence by how well it predicts correctness and whether it is calibrated, leaving open a more fundamental question: what does the confidence signal itself represent? Answer logits may reflect a latent decision variable sufficient to compute normative confidence, or instead a heuristic preference signal that combines the available evidence in a non-Bayesian manner. We address this using statistical decision confidence (SDC), a normative framework from computational neuroscience. Treating the answer-logit difference (LD) as a candidate readout of the latent decision variable, we test the qualitative signatures predicted by SDC. Across three perceptual discrimination tasks and a memory-based decision task, spanning three multimodal non-reasoning models and one reasoning model, LD satisfied these signatures -- including the diagnostic correct/error folded-X pattern -- showing that, in these settings, answer logits behave as monotonic readouts of a latent decision variable rather than heuristic preference scores. In complex visual reasoning, LD continued to predict correctness beyond objective task difficulty, but the full geometric signatures of SDC were absent, illustrating the current boundary of the framework when explicit normative process models are unavailable. These results provide a computational account of confidence in multimodal language models, delineate when answer logits behave as readouts of a latent decision variable, and establish SDC as a unifying framework for studying confidence across biological and artificial intelligence.

Whether neural language models (NLMs) possess the ability to distinguish strings on the basis of their grammaticality remains a debated topic in the computational linguistics literature. Existing evidence has largely relied on probability-based measures, testing whether models assign higher probabilities to grammatical than ungrammatical strings. However, probability comparisons have been criticized as a measure for grammatical knowledge based on the assumption that grammaticality is inherently entangled with likelihood. Model-assigned probability is a function of many related sentence properties, such as lexical frequency, plausibility, and world knowledge. In this work, we move beyond probability-based evaluations and investigate whether grammaticality is encoded in the internal representations of NLMs. Using mass-mean probing, we test whether grammatical and ungrammatical sentences are systematically separated in representational space. We further examine the extent to which these representations are independent of sentence properties that are correlated with grammaticality, as well as their generalization across grammatical phenomena and languages. Our results provide evidence that grammaticality is robustly encoded in sentence representations of a wide range of pretrained NLMs, yielding clear representational separation on the dimension of grammaticality that cannot be fully explained by alternative sentence-level factors. Moreover, this encoding generalizes across a broad range of grammatical phenomena and to some degree, across languages, suggesting that grammaticality constitutes a coherent representational dimension in contemporary NLMs. These findings contribute new evidence to debates about the nature of syntactic knowledge in language models and offer a complementary framework for evaluating grammatical competence that is not dependent on string probabilities alone.