Related papers: Class Algebra for Ontology Reasoning
In-context learning (ICL) enables large language models to perform new tasks by conditioning on a sequence of examples. Most prior work reasonably and intuitively assumes that which examples are chosen has a far greater effect on…
One-class learning is the classic problem of fitting a model to the data for which annotations are available only for a single class. In this paper, we explore novel objectives for one-class learning, which we collectively refer to as…
Relational databases are valuable resources for learning novel and interesting relations and concepts. In order to constraint the search through the large space of candidate definitions, users must tune the algorithm by specifying a…
Some cohomology classes associated with an ideal in a Lie algebra, a Poisson structure on the basic functions algebra of contact structure, its Poisson cohomology and geometric (pre)quantization are considered from the algebraic point of…
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…
It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (CABA's) taking a set to its power-set and, reciprocally, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a…
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the analysis of learning. In this approach, the goal of the…
We present module theory and linear maps as a powerful generalised and computationally efficient framework for the relational data model, which underpins today's relational database systems. Based on universal constructions of modules we…
Lie algebras are an important class of algebras which arise throughout mathematics and physics. We report on the formalisation of Lie algebras in Lean's Mathlib library. Although basic knowledge of Lie theory will benefit the reader, none…
The sharing of ontologies between diverse communities of discourse allows them to compare their own information structures with that of other communities that share a common terminology and semantics - ontology sharing facilitates…
In recent years, several methods have been proposed for explaining individual predictions of deep learning models, yet there has been little study of how to aggregate these predictions to explain how such models view classes as a whole in…
The unification problem in algebras capable of describing sets has been tackled, directly or indirectly, by many researchers and it finds important applications in various research areas--e.g., deductive databases, theorem proving, static…
With the rise of XML as a standard for representing business data, XML data warehouses appear as suitable solutions for Web-based decision-support applications. In this context, it is necessary to allow OLAP analyses over XML data cubes…
We give a polymorphic account of the relational algebra. We introduce a formalism of ``type formulas'' specifically tuned for relational algebra expressions, and present an algorithm that computes the ``principal'' type for a given…
Ontologies represent the conceptual knowledge of a domain. At the core of an ontology is the taxonomy of concepts and subconcepts that represent specific entities, which can be complex to build. In many cases, information is available in…
In modern data analytics, analysts frequently face the challenge of searching for desirable entities by evaluating, for each entity, a collection of its feature relations to derive key analytical properties. This search is challenging…
Rapid growth of documents, web pages, and other types of text content is a huge challenge for the modern content management systems. One of the problems in the areas of information storage and retrieval is the lacking of semantic data.…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…