Related papers: Codd's Theorem for Databases over Semirings
Natural language to SQL (NL2SQL) aims to parse a natural language with a given database into a SQL query, which widely appears in practical Internet applications. Jointly encode database schema and question utterance is a difficult but…
This paper introduces a refinement of the sequent calculus approach called cirquent calculus. While in Gentzen-style proof trees sibling (or cousin, etc.) sequents are disjoint sequences of formulas, in cirquent calculus they are permitted…
The behavior of factorization properties in various ring extensions is a central theme in commutative algebra. Classically, the UFDs are (completely) integrally closed and tend to behave well in standard ring extensions, with the notable…
When data schemata are enriched with expressive constraints that aim at representing the domain of interest, in order to answer queries one needs to consider the logical theory consisting of both the data and the constraints. Query…
Ontology-based data access (OBDA) is a popular paradigm for querying heterogeneous data sources by connecting them through mappings to an ontology. In OBDA, it is often difficult to reconstruct why a tuple occurs in the answer of a query.…
We consider two relations on a $\cap$-semigroup of partial functions of a given set: the inclusion of domains and the semiadjacencity (i.e., the inclusion of the image of the first function into the domain of the second), which…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…
The CAP Theorem is a frequently cited impossibility result in distributed systems, especially among NoSQL distributed databases. In this paper we survey some of the confusion about the meaning of CAP, including inconsistencies and…
A relation algebra is called measurable when its identity is the sum of measurable atoms, and an atom is called measurable if its square is the sum of functional elements. In this paper we show that atomic measurable relation algebras have…
In this paper we present the problem of saturation of a given morphism in the database category DB, which is the base category for the functiorial semantics of the database schema mapping systems used in Data Integration theory. This…
A theorem from control theory relating the Lie algebra generated by vector fields on a manifold to the controllability of the dynamical system is shown to apply to Holonomic Quantum Computation. Conditions for deriving the holonomy algebra…
We study influence of ordinal transformations on results of queries in rank-aware databases which derive their operations with ranked relations from totally ordered structures of scores with infima acting as aggregation functions. We…
The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra.…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
Database analytics algorithms leverage quantifiable structural properties of the data to predict interesting concepts and relationships. The same information, however, can be represented using many different structures and the structural…
In this article I introduce a new communication theory for complex information represented as a direct graph of nodes. In addition, I introduce an application for the theory, a new radical method, embed, that can be used to update object…
Clifford algebras are used for definition of spinors. Because of using spin-1/2 systems as an adequate model of quantum bit, a relation of the algebras with quantum information science has physical reasons. But there are simple mathematical…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
We demonstrate that the notions of derivative representation of a Lie algebra on a vector bundle, of semi-linear representations of a Lie group on a vector bundle, and related concepts, may be understood in terms of representations of Lie…
We propose Cognitive Databases, an approach for transparently enabling Artificial Intelligence (AI) capabilities in relational databases. A novel aspect of our design is to first view the structured data source as meaningful unstructured…