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Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
We present a novel approach to formalise and solve search-based problems using large language models, which significantly improves upon previous state-of-the-art results. We demonstrate the efficacy of this approach on the logic puzzles…
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…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
The ability to summarize and organize knowledge into abstract concepts is key to learning and reasoning. Many industrial applications rely on the consistent and systematic use of concepts, especially when dealing with decision-critical…
Constraint logic grammars provide a powerful formalism for expressing complex logical descriptions of natural language phenomena in exact terms. Describing some of these phenomena may, however, require some form of graded distinctions which…
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…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
Logic-based approaches to AI have the advantage that their behaviour can in principle be explained by providing their users with proofs for the derived consequences. However, if such proofs get very large, then it may be hard to understand…
Answering complex queries over incomplete knowledge graphs (KGs) is a challenging job. Most previous works have focused on learning entity/relation embeddings and simulating first-order logic operators with various neural networks. However,…
Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose $\textbf{Additional Logic Training (ALT)}$, which aims to enhance LLMs' reasoning capabilities by…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
Large language models (LLMs) are increasingly used to solve complex tasks where they must retrieve and compose many pieces of in-context information in long reasoning chains. For many real-world tasks it is hard to accurately gauge how…
Large language models (LLMs) often benefit from verbalized reasoning at inference time, but it remains unclear which aspects of task difficulty these extra reasoning tokens address. To investigate this question, we formalize a framework…
Knowledge representation is a key component to the success of all rule based systems including learning classifier systems (LCSs). This component brings insight into how to partition the problem space what in turn seeks prominent role in…
Large language models (LLMs) make remarkable progress in reasoning tasks. Among different reasoning modes, inductive reasoning, due to its better alignment with human learning, attracts increasing interest. However, research on inductive…
We present a simple linear programming (LP) based method to learn compact and interpretable sets of rules encoding the facts in a knowledge graph (KG) and use these rules to solve the KG completion problem. Our LP model chooses a set of…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…