Related papers: A road to ultrafilter extensions
We present a method for extracting general modules for ontologies formulated in the description logic ALC. A module for an ontology is an ideally substantially smaller ontology that preserves all entailments for a user-specified set of…
In this article we study modules over wild canonical algebras which correspond to extension bundles [9] over weighted projective lines. We prove that all modules attached to extension bundles can be established by matrices with coefficients…
A procedure to extend a superintegrable system into a new superintegrable one is systematically tested for the known systems on $\mathbb E^2$ and $\mathbb S^2$ and for a family of systems defined on constant curvature manifolds. The…
We studied the formation of complex patterns using a variational principle and a standard energy functional. These patterns evolve by letting the system to search for the optimal configuration of a high conductivity channel, that in one…
We show that there exist models $\mathcal M_1$ and $\mathcal M_2$ such that $\mathcal M_1$ elementarily embeds into $\mathcal M_2$ but their ultrafilter extensions $\beta(\mathcal M_1)$ and $\beta(\mathcal M_2)$ are not elementarily…
We study two generalizations of the Rudin-Keisler ordering to ultrafilters on complete Boolean algebras. To highlight the difference between them, we develop new techniques to construct incomparable ultrafilters in this setting.…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
By Lindstr\"{o}m's theorems, the expressive power of first order logic (and similarly continuous logic) is not strengthened without losing some interesting property. Weakening it, is however less harmless and has been payed attention by…
We present three models concerning Tukey types of ultrafilters on $\omega$. The first model is built via a countable support iteration, and we show there is no basically generated ultrafilter in such model. The second and third models are…
The paper contains two natural constructions of extreme hyperspace selections generated by special ordinal decompositions of the underlying space. These constructions are very efficient not only in simplifying arguments but also in…
This paper belongs to the field of probabilistic modal logic, focusing on a comparative analysis of two distinct semantics: one rooted in Kripke semantics and the other in neighbourhood semantics. The primary distinction lies in the…
We give a sufficient condition for Kripke completeness of modal logics enriched with the transitive closure modality. More precisely, we show that if a logic admits what we call definable filtration (ADF), then such an expansion of the…
We study how to infer new choices from prior choices using the framework of choice functions, a unifying mathematical framework for decision-making based on sets of preference orders. In particular, we define the natural (most conservative)…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
This technical report investigates Kripke-style modal type theories, both simply typed and dependently typed. We examine basic meta-theories of the type theories, develop their substitution calculi, and give normalization by evaluation…
We study problems related to indecomposability of modules over certain local finite dimensional trivial extension algebras. We do this by purely combinatorial methods. We introduce the concepts of graph of cyclic modules, of combinatorial…
When predictive models are used to support complex and important decisions, the ability to explain a model's reasoning can increase trust, expose hidden biases, and reduce vulnerability to adversarial attacks. However, attempts at…
We discuss conditions under which certain compactifications of topological spaces can be obtained by composing the ultrafilter space monad with suitable reflectors. In particular, we show that these compactifications inherit their…
We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl. We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of…
Continuous diffusion and flow matching models could represent a powerful alternative to autoregressive approaches for language modelling (LM), as they unlock a host of advantages currently reserved for continuous modalities, including…