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Assessing the reasoning ability of Large Language Models (LLMs) over data remains an open and pressing research question. Compared with LLMs, human reasoning can derive corresponding modifications to the output based on certain kinds of…

In this paper, we present a novel diagnostic framework that integrates Knowledge Graphs (KGs) and Large Language Models (LLMs) to support system diagnostics in high-reliability systems such as nuclear power plants. Traditional diagnostic…

Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…

The integration of reasoning, learning, and decision-making is key to build more general artificial intelligence systems. As a step in this direction, we propose a novel neural-logic architecture, called differentiable logic machine (DLM),…

Large Language Models (LLMs) often exhibit limited logical coherence, mapping premises to conclusions without adherence to explicit inference rules. We propose Proof-Carrying Reasoning with LLMs (PCRLLM), a framework that constrains…

Explainable AI has emerged to be a key component for black-box machine learning approaches in domains with a high demand for reliability or transparency. Examples are medical assistant systems, and applications concerned with the General…

Conjunctive queries play an important role as an expressive query language for Description Logics (DLs). Although modern DLs usually provide for transitive roles, conjunctive query answering over DL knowledge bases is only poorly understood…

Large language models (LLMs) have shown significant progress in reasoning tasks. However, recent studies show that transformers and LLMs fail catastrophically once reasoning problems exceed modest complexity. We revisit these findings…

Large Language Models (LLMs) have shown remarkable reasoning capabilities, while their practical applications are limited by severe factual hallucinations due to limitations in the timeliness, accuracy, and comprehensiveness of their…

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that…

Inductive Knowledge Graph Reasoning (KGR) aims to discover facts in open-domain KGs containing unknown entities and relations, which poses a challenge for KGR models in comprehending uncertain KG components. Existing studies have proposed…

Large language models (LLMs) are deployed on increasingly complex tasks that require multi-step decision-making. Understanding their algorithmic reasoning abilities is therefore crucial. However, we lack a diagnostic benchmark for…

With the continuous expansion of Large Language Models (LLMs) and advances in reinforcement learning, LLMs have demonstrated exceptional reasoning capabilities, enabling them to address a wide range of complex problems. Inspired by these…

Large Language Models (LLMs) have taken Knowledge Representation -- and the world -- by storm. This inflection point marks a shift from explicit knowledge representation to a renewed focus on the hybrid representation of both explicit…

Constraint Logic Programming (CLP) and Hereditary Harrop formulas (HH) are two well known ways to enhance the expressivity of Horn clauses. In this paper, we present a novel combination of these two approaches. We show how to enrich the…

Large language models (LLMs) often struggle with knowledge-intensive tasks due to a lack of background knowledge and a tendency to hallucinate. To address these limitations, integrating knowledge graphs (KGs) with LLMs has been intensively…

Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…

This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…

We propose a novel learning paradigm for Deep Neural Networks (DNN) by using Boolean logic algebra. We first present the basic differentiable operators of a Boolean system such as conjunction, disjunction and exclusive-OR and show how these…

Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, but they exhibit problems with logical consistency in the output they generate. How can we harness LLMs' broad-coverage…