Related papers: R.E. Axiomatization of Conditional Independence
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…
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…
We analyze selected iterated conditionals in the framework of conditional random quantities. We point out that it is instructive to examine Lewis's triviality result, which shows the conditions a conditional must satisfy for its probability…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
It has been recently shown in Jaworski, P., Jelito, D. and Pitera, M. (2024), 'A note on the equivalence between the conditional uncorrelation and the independence of random variables', Electronic Journal of Statistics 18(1), that one can…
The explicit link between Promise Theory and Information Theory, while perhaps obvious, is laid out explicitly here. It's shown how causally related observations of promised behaviours relate to the probabilistic formulation of causal…
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 work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…
Dependence logics are a modern family of logics of independence and dependence which mimic notions of database theory. In this paper, we aim to initiate the study of enumeration complexity in the field of dependence logics and thereby get a…
We consider expressions built up from binary relation names using the operators union, composition, and set difference. We show that it is undecidable to test whether a given such expression $e$ is finitely satisfiable, i.e., whether there…
In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.
In this paper we consider propositional calculi, which are finitely axiomatizable extensions of intuitionistic implicational propositional calculus together with the rules of modus ponens and substitution. We give a proof of undecidability…
I discuss the design of the method of entropic inference as a general framework for reasoning under conditions of uncertainty. The main contribution of this discussion is to emphasize the pragmatic elements in the derivation. More…
The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we…
Rule-based languages lie at the core of several areas of central importance to databases and artificial intelligence such as deductive databases and knowledge representation and reasoning. Disjunctive existential rules (a.k.a. disjunctive…
In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable $\Sigma_{1}$-formulas in PA. Second Paris-Harrington's proof for their independence result is…
We establish the undecidability of conditional affine information inequalities, the undecidability of the conditional independence implication problem with a constraint that one random variable is binary, and the undecidability of the…
The classical propositional assumption-based model is extended to incorporate probabilities for the assumptions. Then it is placed into the framework of evidence theory. Several authors like Laskey, Lehner (1989) and Provan (1990) already…
Modeling of the dependence structure across heterogeneous data is crucial for Bayesian inference since it directly impacts the borrowing of information. Despite the extensive advances over the last two decades, most available proposals…
Axiomatization has been widely used for testing logical implications. This paper suggests a non-axiomatic method, the chase, to test if a new dependency follows from a given set of probabilistic dependencies. Although the chase computation…