Related papers: Labeled Mereological Set Theory
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
Best possible bounds are established for families without s pairwise disjoint members and the more general problem for several families. The results are shown to apply several classical results.
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
We show that the Freiman--Ruzsa theorem, characterising finite sets with bounded doubling, leads to an alternative proof of a characterisation of Meyer sets, that is, relatively dense subsets of Euclidean spaces whose difference sets are…
The semantics as to which set of arguments in a given argumentation graph may be acceptable (acceptability semantics) can be characterised in a few different ways. Among them, labelling-based approach allows for concise and flexible…
Multilabel classification is a relatively recent subfield of machine learning. Unlike to the classical approach, where instances are labeled with only one category, in multilabel classification, an arbitrary number of categories is chosen…
Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…
As mathematical induction is applied to prove statements on natural numbers, {\it continuous induction} (or, {\it real induction}) is a tool to prove some statements in real analysis.(Although, this comparison is somehow an overstatement.)…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set $K\subseteq \mathbb{R}$ is constructed such that every set definable in $(\mathbb{R},<,+,\cdot,K)$ is Borel. In addition, we…
The aim of these lectures is to give a short introduction to forcing. We will avoid metamathematical issues as much as possible and similarly we will avoid performing the actual construction of forcing. We assume familiarity with basic…
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
With a view to establishing measure theoretic approximation properties of Delone sets, we study a setup which arises naturally in the problem of averaging almost periodic functions along exponential sequences. In this setting, we establish…
Following F. William Lawvere, we show that many self-referential paradoxes, incompleteness theorems and fixed point theorems fall out of the same simple scheme. We demonstrate these similarities by showing how this simple scheme encompasses…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…
The aim of this article is to establish basic results in a conditional measure theory. The results are applied to prove that arbitrary kernels and conditional distributions are represented by measures in a conditional set theory. In…
One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these…