Related papers: Logical Tasks for Measuring Extrapolation and Rule…
Inductive reasoning is an essential capability for large language models (LLMs) to achieve higher intelligence, which requires the model to generalize rules from observed facts and then apply them to unseen examples. We present MIRAGE, a…
The paper presents a software tool for analysis and interactive engagement in various logical reasoning tasks. A first feature of the program consists in providing an interface for working with logic-specific repositories of formal…
This invited paper is a passionate pitch for the significance of logic in scientific education. Logic helps focus on the essential core to identify the foundations of ideas and provides corresponding longevity with the resulting approach to…
Previous work indicates that large language models exhibit a significant "English bias", i.e. they often perform better when tasks are presented in English. Interestingly, we have observed that using certain other languages in 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…
This paper proposes a new approach to defining and expressing algorithms: the notion of {\it task logical} algorithms. This notion allows the user to define an algorithm for a task $T$ as a set of agents who can collectively perform $T$.…
Mathematical reasoning skills are essential for general-purpose intelligent systems to perform tasks from grocery shopping to climate modeling. Towards evaluating and improving AI systems in this domain, we propose LILA, a unified…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
Large Language Models (LLMs) have succeeded remarkably in various natural language processing (NLP) tasks, yet their reasoning capabilities remain a fundamental challenge. While LLMs exhibit impressive fluency and factual recall, their…
Mathematical reasoning is regarded as a necessary ability for Language Models (LMs). Recent works demonstrate large LMs' impressive performance in solving math problems. The success is attributed to their Chain-of-Thought (CoT) reasoning…
We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
We introduce a logic for reasoning about evidence that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Large Language Models (LLMs) have shown remarkable performance in various natural language processing tasks but face challenges in mathematical reasoning, where complex problem-solving requires both linguistic understanding and mathematical…
We analyse so-called computable laws, i.e., laws that can be enforced by automatic procedures. These laws should be logically perfect and unambiguous, but sometimes they are not. We use a regulation on road transport to illustrate this…
Mathematical reasoning serves as a cornerstone for assessing the fundamental cognitive capabilities of human intelligence. In recent times, there has been a notable surge in the development of Large Language Models (LLMs) geared towards the…
Large Language Models (LLMs) have demonstrated good performance in many reasoning tasks, but they still struggle with some complicated reasoning tasks including logical reasoning. One non-negligible reason for LLMs' suboptimal performance…
Studying Mathematics requires a synthesis of skills from a multitude of academic disciplines; logical reasoning being chief among them. This paper explores mathematical logical preparedness of students entering first year university…
This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…
With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, large language models (LLMs) have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open…