Related papers: Ruitenburg's Theorem Mechanized and Contextualized
There are several ideal boundaries and completions in General Relativity sharing the topological property of being sequential, i.e., determined by the convergence of its sequences and, so, by some limit operator $L$. As emphasized in a…
We provide a pure algebraic version of the dynamical characterization of Conrad's property. This approach allows dealing with general group actions on totally ordered spaces. As an application, we give a new and somehow constructive proof…
Recent published work has addressed the Shalqvist correspondence problem for non-distributive logics. The natural question that arises is to identify the fragment of first-order logic that corresponds to logics without distribution, lifting…
We introduce a notion of proper morphism for schematic finite spaces and prove the analogue of Grothendieck's finiteness theorem for it by means of the classic result for schemes and general descent arguments. This result also generalizes…
We discuss the possibility of constructing a function that validates the definition or not definition of the partial recursive functions of one variable. This is a topic in computability theory, which was first approached by Alan M. Turing…
In this paper we show that the intuitionistic monotone modal logic $\mathsf{iM}$ has the uniform Lyndon interpolation property (ULIP). The logic $\mathsf{iM}$ is a non-normal modal logic on an intuitionistic basis, and the property ULIP is…
The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but…
We prove refined space-time regularity for the classical stochastic Allen-Cahn equation with logarithmic potential. This allows to establish a random separation property, i.e. that the trajectories of the solution are strictly separated…
Brandenburger, Friedenberg, and Keisler provide an epistemic characterization of iterated admissibility (i.e., iterated deletion of weakly dominated strategies) where uncertainty is represented using LPSs (lexicographic probability…
Robustness is a standard correctness property which intuitively means that if the input to the program changes less than a fixed small amount then the output changes only slightly. This notion is useful in the analysis of rounding error for…
This article presents a bidirectional type system for the Calculus of Inductive Constructions (CIC). It introduces a new judgement intermediate between the usual inference and checking, dubbed constrained inference, to handle the presence…
In rotor walk on a finite directed graph, the exits from each vertex follow a prescribed periodic sequence. Here we consider the case of rotor walk where a particle starts from a designated source vertex and continues until it hits a…
We study a system of intervals $I_1,\ldots,I_k$ on the real line and a continuous map $f$ with $f(I_1 \cup I_2 \cup \ldots \cup I_k)\supseteq I_1 \cup I_2 \cup \ldots \cup I_k$. It's conjectured that there exists a periodic point of period…
The appearance of linear spaces, describing physical quantities by vectors and tensors, is ubiquitous in all of physics, from classical mechanics to the modern notion of local Lorentz invariance. However, as natural as this seems to the…
Causal inference revealing causal dependencies between variables from empirical data has found applications in multiple sub-fields of scientific research. A quantum perspective of correlations holds the promise of overcoming the limitation…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
We introduce a basic intuitionistic conditional logic $\mathsf{IntCK}$ that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that…
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…
The iterative proportional fitting procedure, introduced in 1937 by Kruithof, aims to adjust the elements of an array to satisfy specified row and column sums. Given a rectangular non-negative matrix $X_0$ and two positive marginals $a$ and…
We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a…