Related papers: Inference with Idempotent Valuations
Recently, ranking-based semantics is proposed to rank-order arguments from the most acceptable to the weakest one(s), which provides a graded assessment to arguments. In general, the ranking on arguments is derived from the strength values…
A complete classification is established of Minkowski valuations on lattice polytopes that intertwine the special linear group over the integers and are translation invariant. In the contravariant case, the only such valuations are…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
With the prevalence of deep learning based embedding approaches, recommender systems have become a proven and indispensable tool in various information filtering applications. However, many of them remain difficult to diagnose what aspects…
A new method of constructing translation invariant continuous valuations on convex subsets of the quaternionic space $\HH^n$ is presented. In particular new examples of $Sp(n)Sp(1)$-invariant translation invariant continuous valuations are…
We introduce a canonical structure of a commutative associative filtered algebra with the unit on polynomial smooth valuations, and study its properties. The induced structure on the subalgebra of translation invariant smooth valuations has…
We provide elementary proofs of several results concerning the possible outcomes arising from a fixed profile within the class of positional voting systems. Our arguments enable a simple and explicit construction of paradoxical profiles,…
In this paper will be presented methodology of encoding information in valuations of discrete lattice with some translational invariant constrains in asymptotically optimal way. The method is based on finding statistical description of such…
We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.
Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
Experts do not always feel very, comfortable when they have to give precise numerical estimations of certainty degrees. In this paper we present a qualitative approach which allows for attaching partially ordered symbolic grades to logical…
We introduce two valuation-based deviations on convex bodies. Using a construction that allows us to associate to these deviations "intrinsic" pseudometrics, we establish various results which capture information about the underlying…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
In this paper, we will derive the real roots of certain sets of matrices with real entries. We will also demonstrate that real orthogonal matrices can have real root or be involutory. Eventually, we will represent idempotent matrices in a…
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…
An argument can be seen as a pair consisting of a set of premises and a claim supported by them. Arguments used by humans are often enthymemes, i.e., some premises are implicit. To better understand, evaluate, and compare enthymemes, it is…
This paper deals with valuations of fields of formal meromorphic functions and their residue fields. We explicitly describe the residue fields of the monomial valuations. We also classify all the discrete rank one valuations of fields of…
We investigate how to model exchangeability with choice functions. Exchangeability is a structural assessment on a sequence of uncertain variables. We show how such assessments are a special indifference assessment, and how that leads to a…