Related papers: Realizability Models Separating Various Fan Theore…
Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all…
We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…
Modern statistical learning techniques have often emphasized prediction performance over interpretability, giving rise to "black box" models that may be difficult to understand, and to generalize to other settings. We conceptually divide a…
Whenever P is a proper definable forcing for adding a real, the countable support iteration of P has all the preservation properties it can possibly have, within a wide syntactically identified class of properties.
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Statisticians are largely focused on developing methods that perform well in a frequentist sense -- even the Bayesians. But the widely-publicized replication crisis suggests that these performance guarantees alone are not enough to instill…
In the paper, notions of relative separability for hypergraphs of models of a theory are defined. Properties of these notions and applications to ordered theories are studied: characterizations of relative separability both in a general…
How should we evaluate the quality of generative models? Many existing metrics focus on a model's producibility, i.e. the quality and breadth of outputs it can generate. However, the actual value from using a generative model stems not just…
This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine…
In this paper, we introduce a semantics of realisability for the classical propositional natural deduction and we prove a correctness theorem. This allows to characterize the operational behaviour of some typed terms.
It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable…
For given multivariate functions specified by algebraic, differential or difference equations, the separability problem is to decide whether they satisfy linear differential or difference equations in one variable. In this paper, we will…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
Unlike computation or the numerical analysis of differential equations, simulation does not have a well established conceptual and mathematical foundation. Simulation is an arguable unique union of modeling and computation. However,…
We make use of a finite support product of Jensen forcing to define a model in which there is a countable non-empty lightface $\Pi^1_2$ set of reals containing no ordinal-definable real.
We give an introduction to the realisation theory for infinite-dimensional systems. That is, we show that for any function $G$, analytic and bounded in the right half of the complex plane, there exists operators $A,B,C$ such that…
Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model complete theory $T_0$. We prove that when $T$ admits a model companion $T_+$,…
The past decade has seen a significant interest in learning tractable probabilistic representations. Arithmetic circuits (ACs) were among the first proposed tractable representations, with some subsequent representations being instances of…
We are interested in verifying dynamic properties of finite state reactive systems under fairness assumptions by model checking. The systems we want to verify are specified through a top-down refinement process. In order to deal with the…
The model of interactive Turing machines (ITMs) has been proposed to characterise which stream translations are interactively computable; the model of reactive Turing machines (RTMs) has been proposed to characterise which behaviours are…