Fuzzy reasoning is vital due to the frequent use of imprecise information in
daily contexts. However, the ability of current large language models (LLMs) to
handle such reasoning remains largely uncharted. In this paper, we introduce a
new benchmark, FRoG, for fuzzy reasoning, featuring real-world mathematical
word problems that incorporate generalized quantifiers. Our experimental
findings reveal that fuzzy reasoning continues to pose significant challenges
for LLMs. Moreover, we find that existing methods designed to enhance reasoning
do not consistently improve performance in tasks involving fuzzy logic.
Additionally, our results show an inverse scaling effect in the performance of
LLMs on FRoG. Interestingly, we also demonstrate that strong mathematical
reasoning skills are not necessarily indicative of success on our benchmark.

模糊推理在日常环境中对于使用不精确信息至关重要，本文引入了一个新的基准 FRoG，用于对模糊推理进行评估，实验结果表明大型语言模型在处理模糊推理方面仍面临重大挑战，并且现有的增强推理方法在涉及模糊逻辑的任务中并不一致地提高性能。此外，我们的结果显示了大型语言模型在 FRoG 上的逆比例缩放效应，有趣的是，我们还证明了强大的数学推理技能并不一定意味着在我们的基准测试中取得成功。

FRoG：对大型语言模型中广义量词的模糊推理进行评估

FRoG: Evaluating Fuzzy Reasoning of Generalized Quantifiers in Large  Language Models

Neurosymbolic AI aims to integrate deep learning with symbolic AI. This
integration has many promises, such as decreasing the amount of data required
to train a neural network, improving the explainability and interpretability of
answers given by models and verifying the correctness of trained systems. We
study neurosymbolic learning, where we have both data and background knowledge
expressed using symbolic languages. How do we connect the symbolic and neural
components to communicate this knowledge? One option is fuzzy reasoning, which
studies degrees of truth. For example, being tall is not a binary concept.
Instead, probabilistic reasoning studies the probability that something is true
or will happen. Our first research question studies how different forms of
fuzzy reasoning combine with learning. We find surprising results like a
connection to the Raven paradox stating we confirm "ravens are black" when we
observe a green apple. In this study, we did not use the background knowledge
when we deployed our models after training. In our second research question, we
studied how to use background knowledge in deployed models. We developed a new
neural network layer based on fuzzy reasoning. Probabilistic reasoning is a
natural fit for neural networks, which we usually train to be probabilistic.
However, they are expensive to compute and do not scale well to large tasks. In
our third research question, we study how to connect probabilistic reasoning
with neural networks by sampling to estimate averages, while in the final
research question, we study scaling probabilistic neurosymbolic learning to
much larger problems than before. Our insight is to train a neural network with
synthetic data to predict the result of probabilistic reasoning.

神经符号 AI 旨在将深度学习与符号 AI 相结合，以减少训练神经网络所需的数据量，提高模型给出答案的可解释性和可解性，并验证经过训练的系统的正确性。我们研究神经符号学习，既有使用符号语言表示的数据，也有背景知识。通过模糊推理、概率推理以及训练神经网络来连接符号和神经组件，以交流这一知识。

神经符号学习系统中的优化

Optimisation in Neurosymbolic Learning Systems

Dealing with uncertain, contradicting, and ambiguous information is still a
central issue in Artificial Intelligence (AI). As a result, many formalisms
have been proposed or adapted so as to consider non-monotonicity, with only a
limited number of works and researchers performing any sort of comparison among
them. A non-monotonic formalism is one that allows the retraction of previous
conclusions or claims, from premises, in light of new evidence, offering some
desirable flexibility when dealing with uncertainty. This research article
focuses on evaluating the inferential capacity of defeasible argumentation, a
formalism particularly envisioned for modelling non-monotonic reasoning. In
addition to this, fuzzy reasoning and expert systems, extended for handling
non-monotonicity of reasoning, are selected and employed as baselines, due to
their vast and accepted use within the AI community. Computational trust was
selected as the domain of application of such models. Trust is an ill-defined
construct, hence, reasoning applied to the inference of trust can be seen as
non-monotonic. Inference models were designed to assign trust scalars to
editors of the Wikipedia project. In particular, argument-based models
demonstrated more robustness than those built upon the baselines despite the
knowledge bases or datasets employed. This study contributes to the body of
knowledge through the exploitation of defeasible argumentation and its
comparison to similar approaches. The practical use of such approaches coupled
with a modular design that facilitates similar experiments was exemplified and
their respective implementations made publicly available on GitHub [120, 121].
This work adds to previous works, empirically enhancing the generalisability of
defeasible argumentation as a compelling approach to reason with quantitative
data and uncertain knowledge.

本研究选择计算可信度作为应用领域，评估了异议论证推理的推理能力，并将其与模糊推理和专家系统进行了比较。结果表明，与基线相比，基于异议论证的模型表现更为稳健。这项研究扩展了先前工作，从而提高了异议论证作为处理数据和知识不确定性的一种复杂方法的普适性。