Related papers: On Independence Atoms and Keys
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
A recently proposed axiom system for Andr\'e's central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed…
Inclusion dependencies form one of the most widely used dependency classes. We extend existing results on the axiomatization and computational complexity of their implication problem to two extended variants. We present an alternative…
Primary key (PK) and foreign key (FK) constraints are widely used for query optimization. Knowledge about additional data dependencies, such as order dependencies, enables further substantial performance improvements. However, such…
Can we simplify explanations for software analytics? Maybe. Recent results show that systems often exhibit a "keys effect"; i.e. a few key features control the rest. Just to say the obvious, for systems controlled by a few keys, explanation…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
A new characterization is given to describe implication bases of a closure system in terms of the system's quasi-closed sets. Using this characterization, it is possible to show that groups of implications corresponding to distinct…
The paper investigates properties of the conditional independence relation between pieces of information. This relation is also known in the database theory as embedded multivalued dependency. In 1980, Parker and Parsaye-Ghomi established…
We introduce the concepts of dependence and independence in a very general framework. We use a concept of rank to study dependence and independence. By means of the rank we identify (total) dependence with inability to create more…
We study various notions of dependency in semiring team semantics. Semiring teams are essentially database relations, where each tuple is annotated with some element from a positive semiring. We consider semiring generalizations of several…
We study the properties of algebraic independence and pointwise algebraic independence in a class of continuous theories, the randomizations $T^R$ of complete first order theories $T$. If algebraic and definable closure coincide in $T$,…
Variable independence and decomposability are algorithmic techniques for simplifying logical formulas by tearing apart connections between free variables. These techniques were originally proposed to speed up query evaluation in constraint…
We introduce two approximate variants of inclusion dependencies and examine the axiomatization and computational complexity of their implication problems. The approximate variants allow for some imperfection in the database and differ in…
Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other.…
We study the problem of consistent query answering under primary key violations. In this setting, the relations in a database violate the key constraints and we are interested in maximal subsets of the database that satisfy the constraints,…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…
Dependence logic is a formalism that augments the syntax of first-order logic with dependence atoms asserting that the value of a variable is determined by the values of some other variables, i.e., dependence atoms express functional…
We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…
Integrity constraints (ICs) provide a valuable tool for expressing and enforcing application semantics. However, formulating constraints manually requires domain expertise, is prone to human errors, and may be excessively time consuming,…
We prove two completeness results, one for the extension of dependence logic by a monotone generalized quantifier Q with weak interpretation, weak in the meaning that the interpretation of Q varies with the structures. The second result…