相关论文: Cox's Theorem Revisited

We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system. A first corollary of that result is that incremental stability may be verified by separation of Scaled…

Understanding the Impossibility of a Tie in Hex via Fixed Point Theorems, the Hex Theorem, and Their Equivalence.

The following paper follows on from work by Kamae, and gives a rigorous proof of the Ergodic Theorem, using nonstandard analysis.

In this paper we propose a new perspective on the evolution and history of the idea of mathematical proof. Proofs will be studied at three levels: syntactical, semantical and pragmatical. Computer-assisted proofs will be give a special…

A discussion of different criteria of consistency of quantum field theory from the point of view of physics and mathematics.

Using a quantum like algebraic formulation we give proof of Kochen-Specker theorem. We introduce new criteria in order to account for the contextual nature of measurements in quantum mechanics.

In this article we generalize Cobham theorem to a large class of substitutions including non primitive and non constant length substitutions.

We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…

G\"odel's argument for the First Incompleteness Theorem is, structurally, a proof by contradiction. This article intends to reframe the argument by, first, isolating an additional assumption the argument relies on, and then, second, arguing…

We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.

It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the…

Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

In this short note we report on results on a computational search for a counterexample to the strong coincidence conjecture. In particular, we discuss the method used so that further searches can be conducted.

A generalization of the law of total covariance is presented and proved.

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.

Let (X_n) be a sequence of random variables (with values in a separable metric space) and (N_n) a sequence of random indices. Conditions for X_{N_n} to converge stably (in particular, in distribution) are provided. Some examples, where such…

The article summarizes some developments about a singular versions of the Sturm Comparison and Separation theorems where the coefficients or the interval of definition may be unbounded.