Related papers: Quantitative Linear Logic for Neuro-Symbolic Learn…

Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical…

Qualitative Choice Logic (QCL) and Conjunctive Choice Logic (CCL) are formalisms for preference handling, with especially QCL being well established in the field of AI. So far, analyses of these logics need to be done on a case-by-case…

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…

Neurosymbolic approaches can add robustness to opaque neural systems by incorporating explainable symbolic representations. However, previous approaches have not used formal logic to contextualize queries to and validate outputs of large…

Logics with analogous semantics, such as Fuzzy Logic, have a number of explanatory and application advantages, the most well-known being the ability to help experts develop control systems. From a cognitive systems perspective, such…

Large language models (LLMs) are increasingly used in situations where human values are at stake, such as decision-making tasks that involve reasoning when performed by humans. We investigate the so-called reasoning capabilities of LLMs…

HyLL (Hybrid Linear Logic) and SELL (Subexponential Linear Logic) are logical frameworks that have been extensively used for specifying systems that exhibit modalities such as temporal or spatial ones. Both frameworks have linear logic (LL)…

Despite their linguistic competence, Large Language Models (LLMs) often struggle to reason reliably and flexibly. To identify these shortcomings, we introduce the Non-Linear Reasoning (NLR) dataset, a collection of 55 unique, hand-designed…

We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, covariances collapse, and the learned representation becomes…

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2". For existing System-1-like methods in visual activity understanding, it is crucial to integrate…

The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…

In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…

Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…

The concept of linearity plays a central role in both mathematics and computer science, with distinct yet complementary meanings. In mathematics, linearity underpins functions and vector spaces, forming the foundation of linear algebra and…

Large Language Models (LLMs) still struggle with complex logical reasoning. While previous works achieve remarkable improvements, their performance is highly dependent on the correctness of translating natural language (NL) problems into a…

Background: Neuro-symbolic methods enhance the reliability of neural network classifiers through logical constraints, but they lack native support for ontologies. Objectives: We aim to develop a neuro-symbolic method that reliably outputs…

The idea of representing symbolic knowledge in connectionist systems has been a long-standing endeavour which has attracted much attention recently with the objective of combining machine learning and scalable sound reasoning. Early work…

We present a logic named L_{LF} whose intended use is to formalize properties of specifications developed in the dependently typed lambda calculus LF. The logic is parameterized by the LF signature that constitutes the specification. Atomic…

Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and complex, while the available training data…

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many…