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Grishin proposed enriching the Lambek calculus with multiplicative disjunction (par) and coresiduals. Applications to linguistics were discussed by Moortgat, who spoke of the Lambek-Grishin calculus (LG). In this paper, we adapt Girard's…
We use traced monoidal categories to give a precise general version of "geometry of interaction". We give a number of examples of both "particle-style" and "wave-style" instances of this construction. We relate these ideas to semantics of…
This paper investigates demonstration selection strategies for predicting a user's next point-of-interest (POI) using large language models (LLMs), aiming to accurately forecast a user's subsequent location based on historical check-in…
Large Language Models (LLMs) are typically trained to reflect a relatively uniform set of values, which limits their applicability to tasks that require understanding of nuanced human perspectives. Recent research has underscored the…
Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a…
Advancing large language models (LLMs) for the next point-of-interest (POI) recommendation task faces two fundamental challenges: (i) although existing methods produce semantic IDs that incorporate semantic information, their topology-blind…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
Multi-modal Large Language Models (MLLMs) exhibit impressive problem-solving abilities in various domains, but their visual comprehension and abstract reasoning skills remain under-evaluated. To this end, we present PolyMATH, a challenging…
This paper presents a comprehensive exploration of relation extraction utilizing advanced language models, specifically Chain of Thought (CoT) and Graphical Reasoning (GRE) techniques. We demonstrate how leveraging in-context learning with…
To provide a categorical semantics for co-intuitionistic logic one has to face the fact, noted by Tristan Crolard, that the definition of co-exponents as adjuncts of coproducts does not work in the category Set, where coproducts are…
Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to…
Evaluating multimodal large language models (MLLMs) is fundamentally challenged by the absence of structured, interpretable, and theoretically grounded benchmarks; current heuristically-grouped tasks have vague cognitive targets,…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
With the remarkable success of Multimodal Large Language Models (MLLMs) in perception tasks, enhancing their complex reasoning capabilities has emerged as a critical research focus. Existing models still suffer from challenges such as…
Molecular Relational Learning (MRL), aiming to understand interactions between molecular pairs, plays a pivotal role in advancing biochemical research. Recently, the adoption of large language models (LLMs), known for their vast knowledge…
Pre-trained language models (PLMs) leverage chains-of-thought (CoT) to simulate human reasoning and inference processes, achieving proficient performance in multi-hop QA. However, a gap persists between PLMs' reasoning abilities and those…
A major open question in the theory of Gorenstein liaison is whether or not every arithmetically Cohen--Macaulay subscheme of $\mathbb{P}^n$ can be G-linked to a complete intersection. Migliore and Nagel showed that, if such a scheme is…
Group polarization, the phenomenon where individuals become more extreme after interacting, has been gaining attention, especially with the rise of social media shaping people's opinions. Recent interest has emerged in formal reasoning…
As an emerging task that integrates perception and reasoning, topology reasoning in autonomous driving scenes has recently garnered widespread attention. However, existing work often emphasizes "perception over reasoning": they typically…
Despite strong performance on vision-language tasks, Multimodal Large Language Models (MLLMs) struggle with mathematical problem-solving, with both open-source and state-of-the-art models falling short of human performance on visual-math…