相关论文: Proof of the impossibility of probabilistic induct…

We correct a common (but mistaken) attribution of the evaluation of the probability integral, usually attributed to Poisson, Gauss, or Laplace.

Uncertainty enters into human reasoning and inference in at least two ways. It is reasonable to suppose that there will be roles for these distinct uses of uncertainty also in automated reasoning.

Over one year ago, a very long preprint posted on arXiv [arXiv:1709.03771] and HAL announced a proof of Lehmer's Conjecture (and of other related results). Unfortunately, as was remarked by several specialists, this proof contains a (at…

A review of various definitions of "compatibility" expressed in terms of ordinary probability, and a discussion of the occurrence of incompatibility (and the related phenomenon of interference) in non-quantal probabilistic systems.

We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].

The following is a concise exposition of the conjecture and three of its proofs for the case of positive entropy by D. Rudolph [22] , B. Host [14] and W. Parry [21]. A simpler theorem of R. Lyons [19] - preceding them - is also presented…

This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…

This paper calls attention to the current state of the probability (P) domain which presents weak points at the mathematical level and more significant flaws at the application level. Popper notices how fundamental issues raised in quantum…

This paper shows that one cannot learn the probability of rare events without imposing further structural assumptions. The event of interest is that of obtaining an outcome outside the coverage of an i.i.d. sample from a discrete…

Warning: This paper contains a mistake, rendering the proof of the main theorem invalid. The logic of Bunched Implications (BI) combines both additive and multiplicative connectives, which include two primitive intuitionistic implications.…

This paper proposes new formulas for the probabilities of causation difined by Pearl (2000). Tian and Pearl (2000a, 2000b) showed how to bound the quantities of the probabilities of causation from experimental and observational data, under…

We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter.

We consider several examples of probabilistic existence proofs using compressibility arguments, including some results that involve Lov\'asz local lemma.

Following a paper in which the fundamental aspects of probabilistic inference were introduced by means of a toy experiment, details of the analysis of simulated long sequences of extractions are shown here. In fact, the striking performance…

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

In Mathematical Thought and Its Objects, Charles Parsons argues that our knowledge of the iterability of functions on the natural numbers and of the validity of complete induction is not intuitive knowledge; Brouwer disagrees on both…

In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…

Are P and NP provably inseparable ? Take a look at some unorthodox, guilty mentioned folklore and related unpublished results.

The process of doing Science in condition of uncertainty is illustrated with a toy experiment in which the inferential and the forecasting aspects are both present. The fundamental aspects of probabilistic reasoning, also relevant in real…

We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.