Related papers: On Independence Atoms and Keys

We present associative and causal views of differential privacy. Under the associative view, the possibility of dependencies between data points precludes a simple statement of differential privacy's guarantee as conditioning upon a single…

Data values in a dataset can be missing or anomalous due to mishandling or human error. Analysing data with missing values can create bias and affect the inferences. Several analysis methods, such as principle components analysis or…

Conditional independence, and more generally conditional mutual independence, are central notions in probability theory. In their general forms, they include functional dependence as a special case. In this paper, we tackle two fundamental…

A firm seeks to analyze a dataset and to release the results. The dataset contains information about individual people, and the firm is subject to some regulation that forbids the release of the dataset itself. The regulation also imposes…

A data structure is called history independent if its internal memory representation does not reveal the history of operations applied to it, only its current state. In this paper we study history independence for concurrent data…

In societies increasingly entangled with algorithms, our choices are constantly influenced and shaped by automated systems. This convergence highlights significant concerns for individual autonomy in the age of data-driven AI. It leads to…

The independence of the continuum hypothesis is a result of broad impact: it settles a basic question regarding the nature of N and R, two of the most familiar mathematical structures; it introduces the method of forcing that has become the…

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in (Kontinen and Vaananen 2013) and (Hannula 2015). We prove a characterization…

Semiring semantics for first-order logic provides a way to trace how facts represented by a model are used to deduce satisfaction of a formula. Team semantics is a framework for studying logics of dependence and independence in diverse…

Elementary particles in quantum mechanics (QM) are indistinguishable when sharing the same intrinsic properties and the same quantum state. So, we can consider quantum particles as non-individuals, although non-individuality is usually…

Conditional independence has been widely used in AI, causal inference, machine learning, and statistics. We introduce categoroids, an algebraic structure for characterizing universal properties of conditional independence. Categoroids are…

In this paper independent sets of closure operations are introduced. We characterize minimal keys and antikeys of closure operations in terms of independent sets. We establish an expression on the connection between minimal keys and…

Information theory provides ideas for conceptualising information and measuring relationships between objects. It has found wide application in the sciences, but economics and finance have made surprisingly little use of it. We show that…

Often in language and other areas of cognition, whether two components of an object are identical or not determine whether it is well formed. We call such constraints identity effects. When developing a system to learn well-formedness from…

A probabilistic database with attribute-level uncertainty consists of relations where cells of some attributes may hold probability distributions rather than deterministic content. Such databases arise, implicitly or explicitly, in the…

Integrated information theory (IIT) starts from the existence of consciousness and characterizes its essential properties: every experience is intrinsic, specific, unitary, definite, and structured. IIT then formulates existence and its…

We show a hitherto unexplored consequence of the property of identicity in quantum mechanics. If two identical objects, distinguished by a dynamical variable A, are in certain entangled states of another dynamical variable B, then, for such…

A system is data-independent with respect to a data type X iff the operations it can perform on values of type X are restricted to just equality testing. The system may also store, input and output values of type X. We study model checking…

We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…

A relation consisting of tuples annotated by an element of a monoid K is called a K-relation. A K-database is a collection of K-relations. In this paper, we study entailment of inclusion dependencies over K-databases, where K is a positive…