Related papers: Hypertableau Reasoning for Description Logics
In recent years, Large Language Models (LLMs) have demonstrated remarkable capabilities in parsing textual data and generating code. However, their performance in tasks involving tabular data, especially those requiring symbolic reasoning,…
Explainable AI (XAI) in high-stakes domains should help stakeholders trust and verify system outputs. Yet Chain-of-Thought methods reason before concluding, and logical gaps or hallucinations can yield conclusions that do not reliably align…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
Table-based reasoning with large language models (LLMs) is a promising direction to tackle many table understanding tasks, such as table-based question answering and fact verification. Compared with generic reasoning, table-based reasoning…
Recent large-scale reasoning models have achieved state-of-the-art performance on challenging mathematical benchmarks, yet the internal mechanisms underlying their success remain poorly understood. In this work, we introduce the notion of a…
Large Language Models (LLMs) exhibit persistent logical failures in complex reasoning due to the lack of an internal axiomatic framework. We propose Mathesis, a neuro-symbolic architecture that encodes mathematical states as higher-order…
We present two deductively equivalent calculi for non-deterministic many-valued logics. One is defined by axioms and the other - by rules of inference. The two calculi are obtained from the truth tables of the logic under consideration in a…
Ontologies often require knowledge representation on multiple levels of abstraction, but description logics (DLs) are not well-equipped for supporting this. We propose an extension of DLs in which abstraction levels are first-class citizens…
Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning…
We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and sub-formula property. Properness (i.e. closure under uniform substitution of all parametric…
Ontology is a popular method for knowledge representation in different domains, including the legal domain, and description logics (DL) is commonly used as its description language. To handle reasoning based on inconsistent DL-based legal…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained to a user. If, for instance, a Description Logic reasoner derives a consequence that triggers some action of the overall system, then one can…
Datalog reasoning based on the semina\"ive evaluation strategy evaluates rules using traditional join plans, which often leads to redundancy and inefficiency in practice, especially when the rules are complex. Hypertree decompositions help…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
Explanation and high-order reasoning capabilities are crucial for real-world visual question answering with diverse levels of inference complexity (e.g., what is the dog that is near the girl playing with?) and important for users to…
Large Language Models (LLMs) excel in complex reasoning tasks but struggle with consistent rule application, exception handling, and explainability, particularly in domains like legal analysis that require both natural language…
Description Logics are knowledge representation formalisms that provide, for example, the logical underpinning of the W3C OWL standards. Conjunctive queries, the standard query language in databases, have recently gained significant…
The basic system E of dyadic deontic logic proposed by {\AA}qvist offers a simple solution to contrary-to-duty paradoxes and allows to represent norms with exceptions. We investigate E from a proof-theoretical viewpoint. We propose a…
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…