Related papers: Fixpoint Semantics for Recursive SHACL
Approximation Fixpoint Theory (AFT) is an algebraic framework designed to study the semantics of non-monotonic logics. Despite its success, AFT is not readily applicable to higher-order definitions. To solve such an issue, we devise a…
The paper presents a constructive fixpoint semantics for autoepistemic logic (AEL). This fixpoint characterizes a unique but possibly three-valued belief set of an autoepistemic theory. It may be three-valued in the sense that for a…
The aim of this paper is to provide mathematical foundations of a graph transformation language, called UnCAL, using categorical semantics of type theory and fixed points. About twenty years ago, Buneman et al. developed a graph database…
This article provides a formalization of the W3C Draft Core SHACL Semantics specification using Z notation. This formalization exercise has identified a number of quality issues in the draft. It has also established that the recursive…
Fuzzy logic programming is an established approach for reasoning under uncertainty. Several semantics from classical, two-valued logic programming have been generalized to the case of fuzzy logic programs. In this paper, we show that two of…
Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of non-monotonic logics. In recent work, AFT was generalized to non-deterministic operators, i.e.\ operators whose range are sets…
Graphs have emerged as an important foundation for a variety of applications, including capturing and reasoning over factual knowledge, semantic data integration, social networks, and providing factual knowledge for machine learning…
Shapes Constraint Language (SHACL) is a powerful language for validating RDF data. Given the recent industry attention to Knowledge Graphs (KGs), more users need to validate linked data properly. However, traditional SHACL validation…
Knowledge graphs have emerged as expressive data structures for Web data. Knowledge graph potential and the demand for ecosystems to facilitate their creation, curation, and understanding, is testified in diverse domains, e.g., biomedicine.…
We present a method for the construction of SHACL or ShEx constraints for an existing RDF dataset. It has two components that are used conjointly: an algorithm for automatic schema construction, and an interactive workflow for editing the…
Reasoning in the Semantic Web (SW) commonly uses Description Logics (DL) via OWL2 DL ontologies, or SWRL for variables and Horn clauses. The Rule Interchange Format (RIF) offers more expressive rules but is defined outside RDF and rarely…
SHACL and OWL are two prominent W3C standards for managing RDF data. These languages share many features, but they have one fundamental difference: OWL, designed for inferring facts from incomplete data, makes the open-world assumption,…
Approximation Fixpoint Theory (AFT) was founded in the early 2000s by Denecker, Marek, and Truszczy\'nski as an abstract algebraic framework to study the semantics of non-monotonic logics. Since its early successes, the potential of AFT as…
Abstract argumentation is a reasoning model for evaluating arguments based on various semantics. SCC-recursiveness is a sophisticated property of semantics that provides a general schema for characterizing semantics through the…
A wide variety of nonmonotonic semantics can be expressed as approximators defined under AFT (Approximation Fixpoint Theory). Using traditional AFT theory, it is not possible to define approximators that rely on information computed in…
Argumentation frameworks (AFs) are a foundational tool in artificial intelligence for modeling structured reasoning and conflict. SCC-recursiveness is a well-known design principle in which the evaluation of arguments is decomposed…
Work on knowledge graphs and graph-based data management often focus either on declarative graph query languages or on frameworks for graph analytics, where there has been little work in trying to combine both approaches. However, many…
In this paper we define and study a multi-agent extension of autoepistemic logic (AEL) called distributed autoepistemic logic (dAEL). We define the semantics of dAEL using approximation fixpoint theory, an abstract algebraic framework that…
Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems. We formulate…
We present Shape Expressions (ShEx), an expressive schema language for RDF designed to provide a high-level, user friendly syntax with intuitive semantics. ShEx allows to describe the vocabulary and the structure of an RDF graph, and to…