Related papers: Independence and abstract multiplication
In this work in progress, we discuss independence and interpolation and related topics for classical, modal, and non-monotonic logics.
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 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…
We introduce an atomic formula intuitively saying that given variables are independent from given other variables if a third set of variables is kept constant. We contrast this with dependence logic. We show that our independence atom gives…
We continue the work on the relations between independence logic and the model-theoretic analysis of independence, generalizing the results of [15] and [16] to the framework of abstract independence relations for an arbitrary AEC. We give a…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
We investigate several technical and conceptual questions. Our main subject is the investigation of independence as a ternary relation in the context of non-monotonic logic. In the context of probability, this investigation was started by…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
We present a framework for studying the concept of independence in a general context covering database theory, algebra and model theory as special cases. We show that well-known axioms and rules of independence for making inferences…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
Team semantics is the mathematical basis of modern logics of dependence and independence. In contrast to classical Tarski semantics, a formula is evaluated not for a single assignment of values to the free variables, but on a set of such…
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…
We introduce some new logics of imperfect information by adding atomic formulas corresponding to inclusion and exclusion dependencies to the language of first order logic. The properties of these logics and their relationships with other…
Conditional independence is a crucial concept supporting adequate modelling and efficient reasoning in probabilistics. In knowledge representation, the idea of conditional independence has also been introduced for specific formalisms, such…
We give lower bounds for the degree of multiplicative combinations of iterates of rational functions (with certain exceptions) over a general field, establishing the multiplicative independence of said iterates. This leads to a…
We extend the treatment of functional dependence, the basic concept of dependence logic, to include the possibility of dependence with a limited number of exceptions. We call this approximate dependence. The main result of the paper is a…
Separation logic is a substructural logic which has proved to have numerous and fruitful applications to the verification of programs working on dynamic data structures. Recently, Barthe, Hsu and Liao have proposed a new way of giving…