Related papers: The Imandra Automated Reasoning System (system des…

Reasoning is central to human intelligence, enabling structured problem-solving across diverse tasks. Recent advances in large language models (LLMs) have greatly enhanced their reasoning abilities in arithmetic, commonsense, and symbolic…

Recent studies have demonstrated that Large Language Models (LLMs) have strong mathematical reasoning abilities but rely on hundreds of billions of parameters. To tackle the challenge of poor reasoning in Small Language Models (SLMs),…

Recently, multimodal large language models (MLLMs) have been widely applied to reasoning tasks. However, they suffer from limited multi-rationale semantic modeling, insufficient logical robustness, and are susceptible to misleading…

Automated theorem proving is fundamental to formal methods, and the recent trend is to integrate large language models (LLMs) and proof assistants to form effective proof agents. While existing proof agents show promising performance, they…

This paper introduces the Primender sequence, a novel integer sequence defined by a hybrid rule that combines classical primality with modular digit-based conditions. Specifically, a number n is included in the sequence if it is prime or…

Despite the remarkable coherence of Large Language Models (LLMs), existing evaluation methods often suffer from fluency bias and rely heavily on multiple-choice formats, making it difficult to assess factual accuracy and complex reasoning…

Logical reasoning is central to complex human activities, such as thinking, debating, and planning; it is also a central component of many AI systems as well. In this paper, we investigate the extent to which encoder-only transformer…

Multimodal language models (MLMs) still face challenges in fundamental visual perception tasks where specialized models excel. Tasks requiring reasoning about 3D structures benefit from depth estimation, and reasoning about 2D object…

We show a model construction for a system of higher-order illative combinatory logic $\mathcal{I}_\omega$, thus establishing its strong consistency. We also use a variant of this construction to provide a complete embedding of first-order…

Formal transformations somehow resembling the usual derivative are surprisingly common in computer science, with two notable examples being derivatives of regular expressions and derivatives of types. A newcomer to this list is the…

This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…

In-memory computing (IMC) with single instruction multiple data (SIMD) setup enables memory to perform operations on the stored data in parallel to achieve high throughput and energy saving. To instruct a SIMD IMC hardware to compute a…

In complex inferential tasks like question answering, machine learning models must confront two challenges: the need to implement a compositional reasoning process, and, in many applications, the need for this reasoning process to be…

The currently dominating artificial intelligence and machine learning technology, neural networks, builds on inductive statistical learning. Neural networks of today are information processing systems void of understanding and reasoning…

A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…

Solving mathematical reasoning problems requires not only accurate access to relevant knowledge but also careful, multi-step thinking. However, current retrieval-augmented models often rely on a single perspective, follow inflexible search…

The use of deductive techniques, such as theorem provers, has several advantages in safety verification of hybrid sys- tems; however, state-of-the-art theorem provers require ex- tensive manual intervention. Furthermore, there is often a…

We propose a logic of interactive proofs as a framework for an intuitionistic foundation for interactive computation, which we construct via an interactive analog of the Goedel-McKinsey-Tarski-Artemov definition of Intuitionistic Logic as…

An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…

Although the Retrieval-Augmented Generation (RAG) paradigms can use external knowledge to enhance and ground the outputs of Large Language Models (LLMs) to mitigate generative hallucinations and static knowledge base problems, they still…