Related papers: Topological Subset Space Models for Public Announc…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
Basic pairs and their morphisms are the most elementary framework in which standard topological notions can be defined. We present here a new interpretation of topological concepts as those which can be communicated faithfully between the…
We develop the theory of locally small spaces in a new simple language and apply this simplification to re-build the theory of locally definable spaces over structures with topologies.
Local explainability methods -- those which seek to generate an explanation for each prediction -- are becoming increasingly prevalent due to the need for practitioners to rationalize their model outputs. However, comparing local…
In this paper, we address the logic of knowing why, an example of a non-standard epistemic logic dealing with justified knowledge via a new epistemic operator, under the extensions with ideas from dynamic epistemic logic, namely public…
We consider definable topological spaces of dimension one in o-minimal structures, and state several equivalent conditions for when such a topological space $\left(X,\tau\right)$ is definably homeomorphic to an affine definable space…
We give a necessary and sufficient condition for a one-dimensional regular and Hausdorff topological space definable in a definably complete uniformly locally o-minimal structure of the second kind having definable bounded multiplication…
In this paper we address the problem of well-posedness of multi-dimensional topological Euler-alignment models introduced in \cite{ST-topo}. The main result demonstrates local existence and uniqueness of classical solutions in class…
Representing token embeddings as probability distributions over learned manifolds allows for more flexible contextual inference, reducing representational rigidity while enhancing semantic granularity. Comparative evaluations demonstrate…
(Pre)closure spaces are a generalization of topological spaces covering also the notion of neighbourhood in discrete structures, widely used to model and reason about spatial aspects of distributed systems. In this paper we introduce an…
The aim of this note is to show that every subset of a given topological space is the intersection of a preopen and a preclosed set, therefore $\beta$-locally closed, and that every topological space is $\beta$-submaximal.
In [Van Benthem 2007] the concept of a public announcement is used to study the effect of the iterated elimination of strictly dominated strategies. We offer a simple generalisation of this approach to cover arbitrary strategic games and…
Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification…
Inferential relations govern our concept use. In order to understand a concept it has to be located in a space of implications. There are different kinds of conditions for statements, i.e. that the conditions represent different kinds of…
In this preprint, we present A collaborative human-AI approach to building an inspectable semantic layer for Agentic AI. AI agents first propose candidate knowledge structures from diverse data sources; domain experts then validate,…
The paper proposes a novel architecture for explainable AI based on semantic technologies and AI. We tailor the architecture for the domain of demand forecasting and validate it on a real-world case study. The provided explanations combine…
We develop a logic of secrecy on simplicial models for multi-agent systems. Standard simplicial models provide a geometric semantics for knowledge by representing global states as facets of a chromatic simplicial complex and agents' local…
It is useful to have a criterion for when the predictions of an operational theory should be considered classically explainable. Here we take the criterion to be that the theory admits of a generalized-noncontextual ontological model.…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
Adopting the scientific method a theoretical model is proposed as foundation for information science and technology, extending the existing theory of signaling: a fact f becomes known in a physical system only following the success of a…