Related papers: Merging Ontologies Algebraically
Ordered set (and map) is one of the most used data type. In addition to standard set operations, like insert, delete and contains, it can provide set-set operations such as union, intersection, and difference. Each of these set-set…
Algorithmic decidability is established for two order-theoretic properties of downward closed subsets defined by finitely many obstructions in two infinite posets. The properties under consideration are: (a) being atomic, i.e. not being…
OWL (Web Ontology Language) ontologies which are able to formally represent complex knowledge and support semantic reasoning have been widely adopted across various domains such as healthcare and bioinformatics. Recently, ontology…
This paper augments OBDD with conjunctive decomposition to propose a generalization called OBDD[$\wedge$]. By imposing reducedness and the finest $\wedge$-decomposition bounded by integer $i$ ($\wedge_{\widehat{i}}$-decomposition) on…
Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach…
Large Language Models (LLMs) are increasingly being integrated into various components of Ontology Matching pipelines. This paper investigates the capability of LLMs to perform ontology matching directly on ontology modules and generate the…
The rigidity problem for uniform Roe algebras was recently positively solved. Before its solution was found, there were positive solutions under the assumption of certain technical geometric conditions. In this paper, we introduce weaker…
An operad (this paper deals with non-symmetric operads)may be conceived as a partial algebra with a family of insertion operations, Gerstenhaber's circle-i products, which satisfy two kinds of associativity, one of them involving…
Partial orders and directed acyclic graphs are commonly recurring data structures that arise naturally in numerous domains and applications and are used to represent ordered relations between entities in the domains. Examples are task…
Ontological queries are evaluated against an ontology rather than directly on a database. The evaluation and optimization of such queries is an intriguing new problem for database research. In this paper we discuss two important aspects of…
Ontology alignment is integral to achieving semantic interoperability as the number of available ontologies covering intersecting domains is increasing. This paper proposes OWL2Vec4OA, an extension of the ontology embedding system OWL2Vec*.…
In this paper, we present several improvements in the parallelization of the in-place merge algorithm, which merges two contiguous sorted arrays into one with an O(T) space complexity (where T is the number of threads). The approach divides…
An operad describes a category of algebras and a (co)homology theory for these algebras may be formulated using the homological algebra of operads. A morphism of operads $f:\mathcal{O}\rightarrow\mathcal{P}$ describes a functor allowing a…
Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…
We introduce a novel set-intersection operator called `most-intersection' based on the logical quantifier `most', via natural density of countable sets, to be used in determining the majority characteristic of a given countable (possibly…
The Semantic Web standardizes concept meaning for humans and machines, enabling machine-operable content and consistent interpretation that improves advanced analytics. Reusing ontologies speeds development and enforces consistency, yet…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
The remarkable success of Large Language Models (LLMs) has ushered natural language processing (NLP) research into a new era. Despite their diverse capabilities, LLMs trained on different corpora exhibit varying strengths and weaknesses,…
We present PARIS, an approach for the automatic alignment of ontologies. PARIS aligns not only instances, but also relations and classes. Alignments at the instance-level cross-fertilize with alignments at the schema-level. Thereby, our…