Related papers: Relational Operations in FOLE
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
In this paper, we show how to use a Relational Database Management System in support of Finite Element Analysis. We believe it is a new way of thinking about data management in well-understood applications to prepare them for two major…
Complexity and decidability of logics is a major research area involving a huge range of different logical systems. This calls for a unified and systematic approach for the field. We introduce a research program based on an algebraic…
Analyzing relational languages by their logical expressiveness is well understood. Something not well understood or even formalized is the vague concept of relational query patterns. What are query patterns? And how can we reason about…
We describe Query Defunctionalization which enables off-the-shelf first-order database engines to process queries over first-class functions. Support for first-class functions is characterized by the ability to treat functions like regular…
This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz. Fractional Order Proportional-Integral-Derivative…
We address the problem of learning a distributed representation of entities in a relational database using a low-dimensional embedding. Low-dimensional embeddings aim to encapsulate a concise vector representation for an underlying dataset…
Separate programming models for data transformation (declarative) and computation (procedural) impact programmer ergonomics, code reusability and database efficiency. To eliminate the necessity for two models or paradigms, we propose a…
First-order learning involves finding a clause-form definition of a relation from examples of the relation and relevant background information. In this paper, a particular first-order learning system is modified to customize it for finding…
Exploring relationships across data sources is a crucial optimization for entities recognition. Since databases can store big amount of information with synthetic and organic data, serving all quantity of objects correctly is an important…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
We introduce a relational approach to program synthesis. The key idea is to decompose synthesis tasks into simpler relational synthesis subtasks. Specifically, our representation decomposes a training input-output example into sets of input…
Building on the classroom framework in Heath et al. (2025), this paper proposes FLARE v2 as a recursive, semiotically informed account of how program meaning can be described across abstraction scales in common teaching languages. It…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
We present an ontology for representing workflows over components with Read-Write Linked Data interfaces and give an operational semantics to the ontology via a rule language. Workflow languages have been successfully applied for modelling…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
Many real world systems need to operate on heterogeneous information networks that consist of numerous interacting components of different types. Examples include systems that perform data analysis on biological information networks; social…
Communicating transactions is a form of distributed, non-isolated transactions which provides a simple construct for building concurrent systems. In this paper we develop a logical framework to express properties of the observable behaviour…
A comprehensive model of natural language processing in the brain must accommodate four components: representations, operations, structures and encoding. It further requires a principled account of how these components mechanistically, and…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…