Related papers: Dependence and Independence
We characterize the expressive power of extensions of Dependence Logic and Independence Logic by monotone generalized quantifiers in terms of quantifier extensions of existential second-order logic.
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
The natural unit system, in which the value of fundamental constants such as c and h are set equal to one and all quantities are expressed in terms of a single unit, is usually introduced as a calculational convenience. However, we…
We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms…
Infamously, the finite and unrestricted implication problems for the classes of i) functional and inclusion dependencies together, and ii) embedded multivalued dependencies alone are each undecidable. Famously, the restriction of i) to…
The present paper introduces a modified version of cyclic-monotone independence which originally arose in the context of random matrices, and also introduces its natural analogy called cyclic-Boolean independence. We investigate formulas…
We present a complete finite axiomatization of the unrestricted implication problem for inclusion and conditional independence atoms in the context of dependence logic. For databases, our result implies a finite axiomatization of the…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
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…
We study knowable informational dependence between empirical questions, modeled as continuous functional dependence between variables in a topological setting. We also investigate epistemic independence in topological terms and show that it…
We show that if any four distinct solutions of a rational difference equation are algebraically independent, then any number of distinct solutions to the equation are independent. A nontrivial variant of this result is given for autonomous…
If Nature allowed nonlocal correlations other than those predicted by quantum mechanics, would that contradict some physical principle? Various approaches have been put forward in the past two decades in an attempt to single out quantum…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
In this paper a conditional logic is defined and studied. This conditional logic, Deterministic Bayesian Logic, is constructed as a deterministic counterpart to the (probabilistic) Bayesian conditional. The logic is unrestricted, so that…
We give conditions on a finite set of series of rational numbers to ensure that they are algebraically independent. Specialising our results to polynomials of lower degree, we also obtain new results on irrationality and $mathbb{Q}$-linear…
A dependent theory is a (first order complete theory) T which does not have the independence property. A main result here is: if we expand a model of T by the traces on it of sets definable in a bigger model then we preserve its being…
We define an extension of predicate logic, called Binding Logic, where variables can be bound in terms and in propositions. We introduce a notion of model for this logic and prove a soundness and completeness theorem for it. This theorem is…
Systems are typically made from simple components regardless of their complexity. While the function of each part is easily understood, higher order functions are emergent properties and are notoriously difficult to explain. In networked…
Dependence is an important concept for many tasks in artificial intelligence. A task can be executed more efficiently by discarding something independent from the task. In this paper, we propose two novel notions of dependence in…
We introduce a universal algebraic generalization of de Jongh's notion of dependence for formulas of intuitionistic propositional logic, relating it to a notion of dependence defined by Marczewski for elements of an algebraic structure.…