Related papers: Relational Operations in FOLE
Dedicated to Tony Hoare. In a paper published in 1972 Hoare articulated the fundamental notions of hiding invariants and simulations. Hiding: invariants on encapsulated data representations need not be mentioned in specifications that…
We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory. We suggest a unifying approach using operators where we allow the…
Multivalued linear operators, also known as linear relations, are studied on a specific class of weighted, composition transforms on Fock space. Basic properties of this class of linear relations, such as closed graph, boundedness, complex…
Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…
A prominent approach to implementing ontology-mediated queries (OMQs) is to rewrite into a first-order query, which is then executed using a conventional SQL database system. We consider the case where the ontology is formulated in the…
There exists a wide set of techniques to perform keyword-based search over relational databases but all of them match the keywords in the users' queries to elements of the databases to be queried as first step. The matching process is a…
The essential variables in a finite function $f$ are defined as variables which occur in $f$ and weigh with the values of that function. The number of essential variables is an important measure of complexity for discrete functions. When…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
We introduce a new approach to the description of multi-sorted clones (sets of $k$-tuples of operations of the same arity, closed under coordinatewise composition and containing all projection tuples) on a two-element domain. Leveraging the…
We introduce Compositional Imitation Learning and Execution (CompILE): a framework for learning reusable, variable-length segments of hierarchically-structured behavior from demonstration data. CompILE uses a novel unsupervised,…
One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…
In this paper, we propose causality as a unified framework to explain query answers and non-answers, thus generalizing and extending several previously proposed approaches of provenance and missing query result explanations. We develop our…
The problems that scientists face in creating well designed databases intersect with the concerns of data curation. Entity-relationship modeling and its variants have been the basis of most relational data modeling for decades. However,…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
We describe a general operational method that can be used in the analysis of fractional initial and boundary value problems with additional analytic conditions. As an example, we derive analytic solutions of some fractional generalisation…
Previous work in the context of natural language querying of temporal databases has established a method to map automatically from a large subset of English time-related questions to suitable expressions of a temporal logic-like language,…
Flexible business processes can often be modelled more easily using a declarative rather than a procedural modelling approach. Process mining aims at automating the discovery of business process models. Existing declarative process mining…
Cause-effect relations are an important part of human knowledge. In real life, humans often reason about complex causes linked to complex effects. By comparison, existing formalisms for representing knowledge about causal relations are…
Algebraic effects offer a versatile framework that covers a wide variety of effects. However, the family of operations that delimit scopes are not algebraic and are usually modelled as handlers, thus preventing them from being used freely…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…