相关论文: Multiple-valued Logics

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to…

This is a draft of a chapter on mathematical logic and foundations for an upcoming handbook of computational proof assistants.

We introduce the logic QKSD which is a normal multi-modal logic over finitely many modalities that additionally supports bounded quantification of modalities. An important feature of this logic is that it allows to quantify over the…

This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…

Large Language Models (LLMs) suffer from critical reasoning gaps, including a tendency to hallucinate and poor accuracy in classifying logical fallacies. This limitation stems from their default System 1 processing, which is fast and…

The rise of large language models (LLMs) has enabled us to seek answers to inherently debatable questions on LLM chatbots, necessitating a reliable way to evaluate their ability. However, traditional QA benchmarks assume fixed answers are…

The evaluation of Large Language Models (LLMs) remains challenging due to inconsistency, bias, and the absence of transparent decision criteria in automated judging. We present Debate, Deliberate, Decide (D3), a cost-aware, adversarial…

Large Language Models (LLMs) are increasingly being used in education, yet their correctness alone does not capture the quality, reliability, or pedagogical validity of their problem-solving behavior, especially in mathematics, where…

Evaluating pragmatic reasoning in large language models (LLMs) remains challenging because model behavior can vary depending on evaluation methods. Previous studies suggest that prompt-based judgments may diverge from models' internal…

The importance of taking individual, potentially conflicting perspectives into account when dealing with knowledge has been widely recognised. Many existing ontology management approaches fully merge knowledge perspectives, which may…

Large language models (LLMs) have achieved remarkable successes on various tasks. However, recent studies have found that there are still significant challenges to the logical reasoning abilities of LLMs, which can be categorized into the…

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic,…

Recently, Knowledge Graphs (KGs) have been successfully coupled with Large Language Models (LLMs) to mitigate their hallucinations and enhance their reasoning capability, such as in KG-based retrieval-augmented frameworks. However, current…

Language agents perform complex tasks by using tools to execute each step precisely. However, most existing agents are based on proprietary models or designed to target specific tasks, such as mathematics or multi-hop question answering. We…

Modal probabilistic logics provide a framework for reasoning about probability in modal contexts, involving notions such as knowledge, belief, time, and action. In this paper, we study a particular family of these logics, extending the…

To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution…

We introduce a complete many-valued semantics for basic normal lattice-based modal logic. This relational semantics is grounded on many-valued formal contexts from Formal Concept Analysis. We discuss an interpretation and possible…

Reasoning about real-life events is a unifying challenge in AI and NLP that has profound utility in a variety of domains, while fallacy in high-stake applications could be catastrophic. Able to work with diverse text in these domains, large…

Translation of 'Die Logik Nicht Gleichzeitig Entscheidbarer Aussagen' by Ernst Specker, Dialectica, vol. 14, 239 - 246 (1960).

Uncertainty Quantification (UQ) is a promising approach to improve model reliability, yet quantifying the uncertainty of Large Language Models (LLMs) is non-trivial. In this work, we establish a connection between the uncertainty of LLMs…