Related papers: Hypertableau Reasoning for Description Logics
Description logics are knowledge representation languages that have been designed to strike a balance between expressivity and computational tractability. Many different description logics have been developed, and numerous computational…
Recently, description logic LE-ALC was introduced for reasoning in the semantic environment of enriched formal contexts, and a polynomial-time tableaux algorithm was developed to check the consistency of knowledge bases with acyclic TBoxes.…
Structured reasoning can improve the inference performance of large language models (LLMs), but it also introduces computational cost and control constraints. When additional reasoning structure helps, and when it instead reduces efficiency…
Real-world tables often exhibit irregular schemas, heterogeneous value formats, and implicit relational structure, which degrade the reliability of downstream table reasoning and question answering. Most existing approaches address these…
In this paper we use results from Computable Set Theory as a means to represent and reason about description logics and rule languages for the semantic web. Specifically, we introduce the description logic $\mathcal{DL}\langle…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
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 study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
LLMs have shown impressive progress in natural language processing. However, they still face significant challenges in TableQA, where real-world complexities such as diverse table structures, multilingual data, and domain-specific reasoning…
Developments in semantic web technologies have promoted ontological encoding of knowledge from diverse domains. However, modelling many practical domains requires more expressiveness than what the standard description logics (most…
Fact verification on tabular evidence incentivises the use of symbolic reasoning models where a logical form is constructed (e.g. a LISP-style program), providing greater verifiability than fully neural approaches. However, these systems…
Proving proof-size lower bounds for $\mathbf{LK}$, the sequent calculus for classical propositional logic, remains a major open problem in proof complexity. We shed new light on this challenge by isolating the power of structural rules,…
Large Language Models (LLMs) have demonstrated impressive capability in many natural language tasks. However, the auto-regressive generation process makes LLMs prone to produce errors, hallucinations and inconsistent statements when…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
Fuzzy Description Logics (FDLs) are logic-based formalisms used to represent and reason with vague or imprecise knowledge. It has been recently shown that reasoning in most FDLs using truth values from the interval [0,1] becomes undecidable…
The use of knowledge graphs for grounding agents in real-world Q&A applications has become increasingly common. Answering complex queries often requires multi-hop reasoning and the ability to navigate vast relational structures. Standard…
Concept learning exploits background knowledge in the form of description logic axioms to learn explainable classification models from knowledge bases. Despite recent breakthroughs in neuro-symbolic concept learning, most approaches still…
Standpoint logic is a recently proposed formalism in the context of knowledge integration, which advocates a multi-perspective approach permitting reasoning with a selection of diverse and possibly conflicting standpoints rather than…