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Ivo Düntsch

Publications and source records attributed to Ivo Düntsch.

15 recordsLinked to original sources
arXiv2026

Contact relations on bounded distributive lattices and related structures

We study a discrete representation of contact relations on bounded distributive lattices and some of their reducts. In the course of the paper, we apply ideas and techniques developed by Ivo Düntsch, Dimiter Vakarelov, and Michael Winter, and we show---among others---that contact relations on a distributive join semi-lattice $L$ with the bottom element correspond to reflexive and symmetric relations which are closed in the product of the Stone space of $L$.

math.LO↗
arXiv2026

Towards a logic of affordances

We aim to construct a formal theory of affordances seen as ternary relations. Beginning with a characterization of affordances proposed by James J. Gibson, and utilizing the tools provided by Zdzisław Pawlak's information systems and rough sets, we construct a mathematically precise definition of both crisp and rough affordances. Then, we analyze modal and approximation operators that enable reasoning about affordances in both scenarios.

math.LO↗
arXiv2026

Discrete dualities for some algebras from rough sets

A discrete duality is a relationship between classes of algebras and classes of relational systems (frames) resulting in two representation theorems building on the early work of Jónsson and Tarski, Kripke, and van Benthem. In this section we recall discrete dualities for various types of algebras arising from rough sets.

cs.LO↗
arXiv2025

The fork and its role in unification of closure algebras

We consider the two-pronged fork frame $F$ and the variety $\mathbf{Eq}(B_F)$ generated by its dual closure algebra $B_F$. We describe the finite projective algebras in $\mathbf{Eq}(B_F)$ and give a purely semantic proof that unification in $\mathbf{Eq}(B_F)$ is finitary and not unitary.

cs.LO↗
arXiv2025

A mixed logic with binary operators

In previous work "Betweenness algebras" we introduced and examined the class of betweenness algebras. In the current paper we study a larger class of algebras with binary operators of possibility and sufficiency, the weak mixed algebras. Furthermore, we develop a system of logic with two binary modalities, sound and complete with respect to the class of frames closely related to the aforementioned algebras, and we prove an embedding theorem which solves an open problem from "Betweenness algebras".

math.LO↗
arXiv2025

The Evolution of Rough Sets 1970s-1981

In this note research and publications by Zdzisław Pawlak and his collaborators from 1970s and 1981 are recalled. Focus is placed on the sources of inspiration which one can identify on the basis of those publications. Finally, developments from 1981 related to rough sets and information systems are outlined.

math.HO↗
arXiv2019

Confusion matrices and rough set data analysis

A widespread approach in machine learning to evaluate the quality of a classifier is to cross -- classify predicted and actual decision classes in a confusion matrix, also called error matrix. A classification tool which does not assume distributional parameters but only information contained in the data is based on the rough set data model which assumes that knowledge is given only up to a certain granularity. Using this assumption and the technique of confusion matrices, we define various indices and classifiers based on rough confusion matrices.

cs.LG↗
arXiv2018

Approximation by filter functions

In this exploratory article, we draw attention to the common formal ground among various estimators such as the belief functions of evidence theory and their relatives, approximation quality of rough set theory, and contextual probability. The unifying concept will be a general filter function composed of a basic probability and a weighting which varies according to the problem at hand. To compare the various filter functions we conclude with a simulation study with an example from the area of item response theory.

cs.AI↗
arXiv2018

Representation of lattice frames

The aim of this note is to characterize those doubly ordered frames $\langle X, \leq_1, \leq_2 \rangle$ which are embeddable into the canonical frame of its Urquhart complex algebra.

math.LO↗
arXiv2009

Complex Algebras of Arithmetic

An 'arithmetic circuit' is a labeled, acyclic directed graph specifying a sequence of arithmetic and logical operations to be performed on sets of natural numbers. Arithmetic circuits can also be viewed as the elements of the smallest subalgebra of the complex algebra of the semiring of natural numbers. In the present paper, we investigate the algebraic structure of complex algebras of natural numbers, and make some observations regarding the complexity of various theories of such algebras.

cs.LO↗
arXiv2009

Functions Definable by Numerical Set-Expressions

A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of lifting addition to the level of sets, we speak of "additive circuits". If they are confined to the usual Boolean operations together with the result of lifting addition and multiplication to the level of sets, we speak of "arithmetic circuits". In this paper, we investigate the definability of sets and functions by means of additive and arithmetic circuits, occasionally augmented with additional operations.

cs.LO↗