Despite the remarkable progress in neural models, their ability to generalize—a cornerstone for applications like logical reasoning—remains a critical challenge. We delineate two fundamental aspects of this ability: compositionality, the capacity to abstract atomic logical rules underlying complex inferences, and recursiveness, the aptitude to build intricate representations through iterative application of inference rules. In the literature, these two aspects are often confounded together under the umbrella term of generalization. To sharpen this distinction, we investigated the logical generalization capabilities of pre-trained large language models (LLMs) using the syllogistic fragment as a benchmark for natural language reasoning. We extend classical Aristotelian syllogistic forms to build more complex structures, providing a foundational yet expressive subset of formal logic that supports controlled evaluation of essential reasoning abilities. Our findings reflect this non-trivial benchmark: while LLMs demonstrate reasonable proficiency in recursiveness, they struggle with compositionality. This disparity, however, is not uniform, as a more detailed analysis reveals variability in generalization performance across individual syllogistic types, ranging from near-perfect to significantly lower accuracy. To overcome these limitations and establish a reliable logical prover, we propose a hybrid architecture integrating symbolic reasoning with neural computation. This synergistic interaction enables robust and efficient inference—neural components accelerate processing, while symbolic reasoning ensures completeness. Our experiments show that high efficiency is preserved even with relatively small neural components. As part of our proposed methodology, this analysis provides a rationale and highlights the potential of hybrid models to effectively address key generalization barriers in neural reasoning systems.

The paper presents a tool for automatic marking up of quantifying expressions, their semantic features, and scopes. We explore the idea of using a BERT based neural model for the task (in this case HerBERT, a model trained specifically for Polish, is used). The tool is trained on a recent manually annotated Corpus of Polish Quantificational Expressions (Szymanik and Kieraś, 2022). We discuss how it performs against human annotation and present results of automatic annotation of 300 million sub-corpus of National Corpus of Polish. Our results show that language models can effectively recognise semantic category of quantification as well as identify key semantic properties of quantifiers, like monotonicity. Furthermore, the algorithm we have developed can be used for building semantically annotated quantifier corpora for other languages.

Abstract Ramsey quantifiers are a natural object of study not only for logic and computer science but also for the formal semantics of natural language. Restricting attention to finite models leads to the natural question whether all Ramsey quantifiers are either polynomial-time computable or NP-hard, and whether we can give a natural characterization of the polynomial-time computable quantifiers. In this paper, we first show that there exist intermediate Ramsey quantifiers and then we prove a dichotomy result for a large and natural class of Ramsey quantifiers, based on a reasonable and widely believed complexity assumption. We show that the polynomial-time computable quantifiers in this class are exactly the constant-log-bounded Ramsey quantifiers.

We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifiers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specific informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quantifier in the announcement is positively active (satisfies a form of variety). © 2011 ACM.