arXiv subjects

Manuel Vargas Guzmán

Publications and source records attributed to Manuel Vargas Guzmán.

3 recordsLinked to original sources

arXiv2026

Hybrid Models for Natural Language Reasoning: The Case of Syllogistic Logic

Despite the remarkable progress in neural models, their ability to generalize, a cornerstone for applications such as 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 conflated under the umbrella term of generalization. To sharpen this distinction, we investigate the logical generalization capabilities of LLMs using the syllogistic fragment as a benchmark for natural language reasoning. We extend classical syllogistic forms to construct more complex structures, yielding a foundational yet expressive subset of formal logic that supports controlled evaluation of essential reasoning abilities. Our findings on this non-trivial benchmark show that, while LLMs demonstrate reasonable proficiency in recursiveness, they struggle with compositionality. This disparity is not uniform, as a more detailed analysis reveals substantial variability in generalization performance across individual syllogistic types, ranging from near-perfect accuracy to significantly lower performance. 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 guarantees completeness. Our experiments further show that high efficiency is preserved even when using relatively small neural components. Overall, our analysis provides both a rationale for hybrid neuro-symbolic approaches and evidence of their potential to address key generalization barriers in neural reasoning systems.

cs.CL↗

arXiv2026

Teaching Small Language Models to Learn Logic through Meta-Learning

Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the problem as premise selection and construct controlled datasets to isolate logical competence. Beyond evaluation, an open challenge is enabling LLMs to acquire abstract inference patterns that generalize to novel structures. We propose to apply few-shot meta-learning to this domain, thereby encouraging models to extract rules across tasks rather than memorize patterns within tasks. Although meta-learning has been little explored in the context of logic learnability, our experiments show that it is effective: small models (1.5B-7B) fine-tuned with meta-learning demonstrate strong gains in generalization, with especially pronounced benefits in low-data regimes. These meta-learned models outperform GPT-4o and o3-mini on our syllogistic reasoning task.

cs.CL↗

arXiv2012

Model-Checking Process Equivalences

Process equivalences are formal methods that relate programs and system which, informally, behave in the same way. Since there is no unique notion of what it means for two dynamic systems to display the same behaviour there are a multitude of formal process equivalences, ranging from bisimulation to trace equivalence, categorised in the linear-time branching-time spectrum. We present a logical framework based on an expressive modal fixpoint logic which is capable of defining many process equivalence relations: for each such equivalence there is a fixed formula which is satisfied by a pair of processes if and only if they are equivalent with respect to this relation. We explain how to do model checking, even symbolically, for a significant fragment of this logic that captures many process equivalences. This allows model checking technology to be used for process equivalence checking. We show how partial evaluation can be used to obtain decision procedures for process equivalences from the generic model checking scheme.

cs.LO↗