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The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a…
We expand the theoretical background of the recently introduced superadditive and subadditive transformations of aggregation functions $A$. Necessary and sufficient conditions ensuring that a transformation of a proper aggregation function…
By using variational methods, the existence of infinitely many solutions for a nonlinear algebraic system with a parameter is established in presence of a perturbed Lipschitz term. Our goal was achieved requiring an appropriate behavior of…
Instrumental variables (IVs) are widely used to study the causal effect of an exposure on an outcome in the presence of unmeasured confounding. IVs require an instrument, a variable that is (A1) associated with the exposure, (A2) has no…
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e.,…
In order to make argumentation-based inference contestable, it is crucial to explain what changes can achieve a desired (instead of the contested) inference result. To this end, we introduce strength change explanations for quantitative…
A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.
A Wiener-type condition for the continuity at the boundary points of Q-minima, is established, in terms of the divergence of a suitable Wiener integral.
In this paper we study the complexity of solving a problem when a solution of a similar instance is known. This problem is relevant whenever instances may change from time to time, and known solutions may not remain valid after the change.…
The usual advantages put forward for including nullability declarations in the type systems of programming languages are that they improve program reliability or performance. But there is another, entirely different, reason for doing so. In…
In this work, we prove the existence of solutions for a tripled system of integral equations using some new results of fixed point theory associated with measure of noncompactness. These results extend some previous works in the literature,…
In this paper we formulate the problem of inference under incomplete information in very general terms. This includes modelling the process responsible for the incompleteness, which we call the incompleteness process. We allow the process…
Necessary and sufficient condition for the existence of a minimum uncertainty state for an arbitrary pair of observables is given.
The Right to Explanation is an important regulatory principle that allows individuals to request actionable explanations for algorithmic decisions. However, several technical challenges arise when providing such actionable explanations in…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases these inequalities are tight in certain limits. As a consequence, we deduce a tight double…
We give a necessary and sufficient condition for the existence of a local solution of the inverse problem of calculus of variations in terms of the identical vanishing of the variation of a functional on an extended space (with the number…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
Decidability and synthesis of inductive invariants ranging in a given domain play an important role in many software and hardware verification systems. We consider here inductive invariants belonging to an abstract domain $A$ as defined in…
Matrix regularity is a key to various problems in applied mathematics. The sufficient conditions, used for checking regularity of interval parametric matrices, usually fail in case of large parameter intervals. We present necessary and…