Related papers: On variable non-dependence of first-order formulas

Measuring a strength of dependence of random variables is an important problem in statistical practice. In this paper, we propose a new function valued measure of dependence of two random variables. It allows one to study and visualize…

Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…

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…

Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…

While modal extensions of decidable fragments of first-order logic are usually undecidable, their monodic counterparts, in which formulas in the scope of modal operators have at most one free variable, are typically decidable. This only…

In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…

The original development of Shapley values for prediction explanation relied on the assumption that the features being described were independent. If the features in reality are dependent this may lead to incorrect explanations. Hence,…

In this paper, we derive an optimal first-order Taylor-like formula. In a seminal paper [14], we introduced a new first-order Taylor-like formula that yields a reduced remainder compared to the classical Taylor's formula. Here, we relax the…

We study the reactive synthesis problem for distributed systems with an unbounded number of participants interacting with an uncontrollable environment. Executions of those systems are modeled by data words, and specifications are given as…

We establish coNExpTime-completeness of the problem of deciding order-invariance of a given two variable first-order formula, improving and significantly simplifying coTwoNExpTime bound by Zeume and Harwath.

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…

Noninterference provides a control over information flow in a system for ensuring confidentiality and integrity properties. In the literature this notion has been well studied as transitive noninterference and intransitive noninterference.…

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…

The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…

In this paper, we propose to learn sources independence in order to choose the appropriate type of combination rules when aggregating their beliefs. Some combination rules are used with the assumption of their sources independence whereas…

Both propositional dependence logic and inquisitive logic are expressively complete. As a consequence, every formula with intuitionistic disjunction or intuitionistic implication can be translated equivalently into a formula in the language…

Our goal is to show that the standard model-theoretic concept of types can be applied in the study of order-invariant properties, i.e., properties definable in a logic in the presence of an auxiliary order relation, but not actually…

The boundary conditions of the bosonic string theory in non-zero $B$-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the…

We prove that adding upwards closed first-order dependency atoms to first-order logic with team semantics does not increase its expressive power (with respect to sentences), and that the same remains true if we also add constancy atoms. As…

Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…