Related papers: Solomonoff Induction Violates Nicod's Criterion
We consider a class of Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part, and we analyze their numerical discretizations by symplectic methods when the initial value is small in Sobolev norms.…
Cyclic proof theory breaks tradition by allowing certain infinite proofs: those that can be represented by a finite graph, while satisfying a soundness condition. We reconcile cyclic proofs with traditional finite proofs: we extend abstract…
G\"odel's second incompleteness theorem is proved for Herbrand consistency of some arithmetical theories with bounded induction, by using a technique of logarithmic shrinking the witnesses of bounded formulas, due to Z. Adamowicz [Herbrand…
Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the…
The black hole no-hair theorem is traditionally derived from the uniqueness theorems of general relativity. We show that a quantitative form follows from unitarity together with the standard semiclassical assumptions of horizon causality…
We show that Brown's lemma is equivalent to Sigma02-induction over RCA0* and that the finite version of Brown's lemma is provable in RCA0 but not in RCA0*.
This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…
Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…
We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the…
Economic theory implies strong limitations on what types of consumption behavior are considered rational. Rationality implies that the Slutsky matrix, which captures the substitution effects of compensated price changes on demand for…
A group is surjunctive if every injective cellular automaton on it is also surjective. Gottschalk famously conjectured that all groups are surjunctive. This remains a central open problem in symbolic dynamics and descriptive set theory.…
In theorem provers based on dependent type theory such as Coq and Lean, induction is a fundamental proof method and induction tactics are omnipresent in proof scripts. Yet the ergonomics of existing induction tactics are not ideal: they do…
Observability is a fundamental structural property of any dynamic system and describes the possibility of reconstructing the state that characterizes the system from observing its inputs and outputs. Despite the huge effort made to study…
Semiclassical reasoning suggests that the process by which an object collapses into a black hole and then evaporates by emitting Hawking radiation may destroy information, a problem often referred to as the black hole information paradox.…
We prove, and mechanize in Rocq, an abstract obstruction theorem for primitive closure predicates, defined as $C : \mathsf{Form} \to \mathsf{Prop}$ over the closed implication-falsity fragment $A,B ::= \bot \mid A \to B$. Two structurally…
We consider the generalized Fibonacci counting problem with rabbits that become fertile at age $f$ and die at age $d$, with $1<=f<=d$ and $d$ finite or infinite. We provide a simple proof, based exclusively on a counting argumentation, for…
We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation…
In this paper, we investigate a stochastic Hardy-Littlewood-Sobolev inequality. Due to the stochastic nature of the inequality, the relation between the exponents of intgrability is modified. This modification can be understood as a…
Theories that attempt to explain the observed cosmic acceleration by modifying general relativity all introduce a new scalar degree of freedom that is active on large scales, but is screened on small scales to match experiments. We show…
We consider the problem of intruder deduction in security protocol analysis: that is, deciding whether a given message M can be deduced from a set of messages Gamma under the theory of blind signatures and arbitrary convergent equational…