Related papers: On the logical skills of large language models: ev…

We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…

Although large language models (LLMs) have apparently acquired a certain level of grammatical knowledge and the ability to make generalizations, they fail to interpret negation, a crucial step in Natural Language Processing. We try to…

Large language models (LLMs) with billions of parameters exhibit in-context learning abilities, enabling few-shot learning on tasks that the model was not specifically trained for. Traditional models achieve breakthrough performance on…

The profusion of knowledge encoded in large language models (LLMs) and their ability to apply this knowledge zero-shot in a range of settings makes them promising candidates for use in decision-making. However, they are currently limited by…

We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial…

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their…

The reasoning abilities of large language models (LLMs) are the topic of a growing body of research in AI and cognitive science. In this paper, we probe the extent to which twenty-nine LLMs are able to distinguish logically correct…

We present a new system S for handling uncertainty in a quantified modal logic (first-order modal logic). The system is based on both probability theory and proof theory. The system is derived from Chisholm's epistemology. We concretize…

Large language models (LLMs) have demonstrated remarkable capabilities in problem-solving. However, their proficiency in solving mathematical problems remains inadequate. We propose MathScale, a simple and scalable method to create…

Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…

Large Language Models (LLMs) are increasingly utilized in AI-driven educational instruction and assessment, particularly within mathematics education. The capability of LLMs to generate accurate answers and detailed solutions for math…

Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…

The planning ability of Large Language Models (LLMs) has garnered increasing attention in recent years due to their remarkable capacity for multi-step reasoning and their ability to generalize across a wide range of domains. While some…

Formal logic enables computers to reason in natural language by representing sentences in symbolic forms and applying rules to derive conclusions. However, in what our study characterizes as "rulebreaker" scenarios, this method can lead to…

Large language models (LLMs), especially when instruction-tuned for chat, have become part of our daily lives, freeing people from the process of searching, extracting, and integrating information from multiple sources by offering a…

Human reasoning involves different strategies, each suited to specific problems. Prior work shows that large language model (LLMs) tend to favor a single reasoning strategy, potentially limiting their effectiveness in diverse reasoning…

Pretrained large Language Models (LLMs) are able to answer questions that are unlikely to have been encountered during training. However a diversity of potential applications exist in the broad domain of reasoning systems and considerations…

We argue that the language of Zermelo Fraenkel set theory with definitions and partial functions provides the most promising bedrock semantics for communicating and sharing mathematical knowledge. We then describe a syntactic sugaring of…

The applications of large language models (LLMs) have been widely spread across all domains. However, the basic abilities such as the controllability of LLMs are still limited. To address this, we propose "Self-controller", a novel agentic…

We describe two systems currently being developed that use large language models for the automatized correction of (i) exercises in translating back and forth between natural language and the languages of propositional logic and first-order…