相关论文: Matching, Merging and Structural Properties of Dat…
Recent work on database application development platforms has sought to include a declarative formulation of a conceptual data model in the application code, using annotations or attributes. Some recent work has used metadata to include the…
The increasing demand for deep neural inference within database environments has driven the emergence of AI-native DBMSs. However, existing solutions either rely on model-centric designs requiring developers to manually select, configure,…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
Within the context of the mathematical formulation of Merge and the Strong Minimalist Thesis, we present a mathematical model of the morphology-syntax interface. In this setting, morphology has compositional properties responsible for word…
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
New applications of data mining, such as in biology, bioinformatics, or sociology, are faced with large datasetsstructured as graphs. We introduce a novel class of tree-shapedpatterns called tree queries, and present algorithms for…
Morphisms are homomorphisms under the concatenation operation of the set of words over a finite set. Changing the elements of the finite set does not essentially change the morphism. We propose a way to select a unique representing member…
In \cite{Spi}, we developed a category of databases in which the schema of a database is represented as a simplicial set. Each simplex corresponds to a table in the database. There, our main concern was to find a categorical formulation of…
We introduce a deep multitask architecture to integrate multityped representations of multimodal objects. This multitype exposition is less abstract than the multimodal characterization, but more machine-friendly, and thus is more precise…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Derivations provide a way of transporting ideas from the calculus of manifolds to algebraic settings where there is no sensible notion of limit. In this paper, we consider derivations in certain monoidal categories, called codifferential…
It is commonly accepted in the practice of on-line analytical processing of databases that the multidimensional database organization is less scalable than the relational one. It is easy to see that the size of the multidimensional…
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
Database system architectures are undergoing revolutionary changes. Algorithms and data are being unified by integrating programming languages with the database system. This gives an extensible object-relational system where non-procedural…
AI-Powered database (AI-DB) is a novel relational database system that uses a self-supervised neural network, database embedding, to enable semantic SQL queries on relational tables. In this paper, we describe an architecture and…
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language…
We propose a new approach to querying graph databases. Our approach balances competing goals of expressive power, language clarity and computational complexity. A distinctive feature of our approach is the ability to express properties of…
Recent years have witnessed a steep increase in linguistic databases capturing syntactic variation. We survey and describe 21 publicly available morpho-syntactic databases, focusing on such properties as data structure, user interface,…
We propose the design of novel categorical generative AI architectures (GAIAs) using topos theory, a type of category that is ``set-like": a topos has all (co)limits, is Cartesian closed, and has a subobject classifier. Previous theoretical…
Morphisms, structure preserving maps, are everywhere in Mathematics as useful tools for thinking and problem solving, or as objects to study. Here, we argue that the idea of operations being compatible across two domains goes beyond its…