Related papers: logLTN: Differentiable Fuzzy Logic in the Logarith…

With the rapid advancement of large language models (LLMs), natural language processing (NLP) has achieved remarkable progress. Nonetheless, significant challenges remain in handling texts with ambiguity, polysemy, or uncertainty. We…

Recent years have witnessed the rapid development of Neuro-Symbolic (NeSy) AI systems, which integrate symbolic reasoning into deep neural networks. However, most of the existing benchmarks for NeSy AI fail to provide long-horizon reasoning…

Despite the extensive investment and impressive recent progress at reasoning by similarity, deep learning continues to struggle with more complex forms of reasoning such as non-monotonic and commonsense reasoning. Non-monotonicity is a…

Semantic segmentation is a fundamental task in medical image analysis, aiding medical decision-making by helping radiologists distinguish objects in an image. Research in this field has been driven by deep learning applications, which have…

Fuzzy logic programming is a growing declarative paradigm aiming to integrate fuzzy logic into logic programming. One of the most difficult tasks when specifying a fuzzy logic program is determining the right weights for each rule, as well…

We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and…

One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model…

A large class of Neural-Symbolic (NeSy) methods employs a machine learner to process the input entities, while relying on a reasoner based on First-Order Logic to represent and process more complex relationships among the entities. A…

The field of neuro-symbolic artificial intelligence (NeSy), which combines learning and reasoning, has recently experienced significant growth. There now are a wide variety of NeSy frameworks, each with its own specific language for…

Type-1 and Interval Type-2 (IT2) Fuzzy Logic Systems (FLS) excel in handling uncertainty alongside their parsimonious rule-based structure. Yet, in learning large-scale data challenges arise, such as the curse of dimensionality and training…

Recent work on neuro-symbolic inductive logic programming has led to promising approaches that can learn explanatory rules from noisy, real-world data. While some proposals approximate logical operators with differentiable operators from…

Neurosymbolic (NeSy) AI aims to combine the strengths of neural architectures and symbolic reasoning to improve the accuracy, interpretability, and generalization capability of AI models. While logic inference on top of subsymbolic modules…

Recent years have witnessed the success of deep neural networks in many research areas. The fundamental idea behind the design of most neural networks is to learn similarity patterns from data for prediction and inference, which lacks the…

In this paper we introduce and study semigroups of operators on spaces of fuzzy-number-valued functions, and various applications to fuzzy differential equations are presented. Starting from the space of fuzzy numbers, many new spaces…

Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training.…

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…

The goal of neuro-symbolic AI is to integrate symbolic and subsymbolic AI approaches, to overcome the limitations of either. Prominent systems include Logic Tensor Networks (LTN) or DeepProbLog, which offer neural predicates and end-to-end…

Deep Learning (DL) techniques have achieved remarkable successes in recent years. However, their ability to generalize and execute reasoning tasks remains a challenge. A potential solution to this issue is Neuro-Symbolic Integration (NeSy),…

In this paper, we introduce Neural Probabilistic Soft Logic (NeuPSL), a novel neuro-symbolic (NeSy) framework that unites state-of-the-art symbolic reasoning with the low-level perception of deep neural networks. To model the boundary…

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and…