Related papers: A Cointuitionistic Adjoint Logic

Large language models (LLMs) exhibit remarkable in-context learning (ICL) capabilities. However, the underlying working mechanism of ICL remains poorly understood. Recent research presents two conflicting views on ICL: One emphasizes the…

Linear/non-linear (LNL) models, as described by Benton, soundly model a LNL term calculus and LNL logic closely related to intuitionistic linear logic. Every such model induces a canonical enrichment that we show soundly models a LNL lambda…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

Chain-of-Thought (CoT) prompting has been widely recognized for its ability to enhance reasoning capabilities in large language models (LLMs). However, our study reveals a surprising contradiction to this prevailing perspective within the…

Integrating logical reasoning and machine learning by approximating logical inference with differentiable operators is a widely used technique in Neuro-Symbolic systems. However, some differentiable operators could bring a significant bias…

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…

We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…

Cobordism categories are known to be compact closed. They can therefore be used to define non-degenerate models of multiplicative linear logic by combining the Int construction with double glueing. In this work we detail such construction…

Linearly distributive categories were introduced to model the tensor/par fragment of linear logic, without resorting to the use of negation. Linear bicategories are the bicategorical version of linearly distributive categories. Essentially,…

Recent advancements highlight the success of instruction tuning with large language models (LLMs) utilizing Chain-of-Thought (CoT) data for mathematical reasoning tasks. Despite the fine-tuned LLMs, challenges persist, such as incorrect,…

Large language models (LLMs), inspired by neuroscience, exhibit behaviors that often evoke a sense of personality and intelligence-yet the mechanisms behind these effects remain elusive. Here, we operationalize Conceptual Blending Theory…

Instance-incremental learning (IIL) focuses on learning continually with data of the same classes. Compared to class-incremental learning (CIL), the IIL is seldom explored because IIL suffers less from catastrophic forgetting (CF). However,…

In-context Learning (ICL) is an emerging few-shot learning paradigm on Language Models (LMs) with inner mechanisms un-explored. There are already existing works describing the inner processing of ICL, while they struggle to capture all the…

The ability to recognize patterns from examples and apply them to new ones is a primal ability for general intelligence, and is widely studied by psychology and AI researchers. Many benchmarks have been proposed to measure such ability for…

We propose an explainable approach for relation extraction that mitigates the tension between generalization and explainability by jointly training for the two goals. Our approach uses a multi-task learning architecture, which jointly…

In-context learning (ICL) allows large models to adapt to tasks using a few examples, yet its extension to vision-language models (VLMs) remains fragile. Our analysis reveals that the fundamental limitation lies in an inductive gap, models…

Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal…

We study the relationship between cartesian bicategories and a specialisation of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both provide different ways of abstracting the structural properties of logical systems: the…

This work presents the deductive system Double Propositional Logic, LD, along with the semantics of possible worlds that characterize it. LD includes an alternate affirmation operator and an alternate negation operator and is not valid for…

While Large Language Models (LLMs) have emerged with remarkable capabilities in complex tasks through Chain-of-Thought reasoning, practical resource constraints have sparked interest in transferring these abilities to smaller models.…