Related papers: Reasoning with Individuals for the Description Log…
We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHOQ, which extends the basic description logic ALC with transitive roles, hierarchies of…
Combining knowledge and beliefs of autonomous peers in distributed settings, is a ma- jor challenge. In this paper we consider peers that combine ontologies and reason jointly with their coupled knowledge. Ontologies are within the SHIQ…
We give the first ExpTime (complexity-optimal) tableau decision procedure for checking satisfiability of a knowledge base in the description logic SHIQ when numbers are coded in unary. Our procedure is based on global state caching and…
Description Logics (DLs) are suitable, well-known, logics for managing structured knowledge. They allow reasoning about individuals and well defined concepts, i.e., set of individuals with common properties. The experience in using DLs in…
Conjunctive query answering over expressive Horn Description Logic ontologies is a relevant and challenging problem which, in some cases, can be addressed by application of the chase algorithm. In this paper, we define a novel acyclicity…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and,…
In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…
The Bhatt Conjectures framework introduces rigorous, hierarchical benchmarks for evaluating AI reasoning and understanding, moving beyond pattern matching to assess representation invariance, robustness, and metacognitive self-awareness.…
This thesis concerns the development of a framework that facilitates the design and analysis of formal systems. Specifically, this framework provides a specification language which supports the concise and direct description of formal…
The emergence of tools based on artificial intelligence has also led to the need of producing explanations which are understandable by a human being. In most approaches, the system is considered a black box, making it difficult to generate…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
An important aspect of artificial intelligence (AI) is the ability to reason in a step-by-step "algorithmic" manner that can be inspected and verified for its correctness. This is especially important in the domain of question answering…
Reasoning about exceptions in ontologies is nowadays one of the challenges the description logics community is facing. The paper describes a preferential approach for dealing with exceptions in Description Logics, based on the rational…
Concept induction, which is based on formal logical reasoning over description logics, has been used in ontology engineering in order to create ontology (TBox) axioms from the base data (ABox) graph. In this paper, we show that it can also…
Explainable AI (XAI) aims to improve user understanding and decisions when using AI models. However, despite innovations in XAI, recent user evaluations reveal that this goal remains elusive. Understanding human cognition can help explain…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
Relational descriptions have been used in formalizing diverse computational notions, including, for example, operational semantics, typing, and acceptance by non-deterministic machines. We therefore propose a (restricted) logical theory…
In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part…
Many ontologies, i.e., Description Logic (DL) knowledge bases, have been developed to provide rich knowledge about various domains. An ontology consists of an ABox, i.e., assertion axioms between two entities or between a concept and an…