Related papers: The Force of Proof by Which Any Argument Prevails

The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…

Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof…

This article is an extension of the results of two earlier articles. In [J. Schubert, On nonspecific evidence, Int. J. Intell. Syst. 8 (1993) 711-725] we established within Dempster-Shafer theory a criterion function called the metaconflict…

Across machine learning (ML) sub-disciplines researchers make mathematical assumptions to facilitate proof-writing. While such assumptions are necessary for providing mathematical guarantees for how algorithms behave, they also necessarily…

Bayesian inference gets its name from *Bayes's theorem*, expressing posterior probabilities for hypotheses about a data generating process as the (normalized) product of prior probabilities and a likelihood function. But Bayesian inference…

Bohr's interpretation of quantum mechanics has been criticized as incoherent and opportunistic, and based on doubtful philosophical premises. If so Bohr's influence, in the pre-war period of 1927-1939, is the harder to explain, and the…

For several decades, legal and scientific scholars have argued that conclusions from forensic examinations should be supported by statistical data and reported within a probabilistic framework. Multiple models have been proposed to quantify…

Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2],…

We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988],…

In the absence of empirical confirmation, scientists may judge a theory's chances of being viable based on a wide range of arguments. The paper argues that such arguments can differ substantially with regard to their structural similarly to…

The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…

In this article we provide a rebuttal against the possible perception that a single number, such as the Likelihood Ratio, can provide an objective, authoritative or definitive weight of evidence. We also illustrate the extent to which…

We introduce a new approach to modeling uncertainty based on plausibility measures. This approach is easily seen to generalize other approaches to modeling uncertainty, such as probability measures, belief functions, and possibility…

When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…

The Weak Law of Large Numbers is traced chronologically from its inception as Jacob Bernoulli's Theorem in 1713, through De Moivre's Theorem, to ultimate forms due to Uspensky and Khinchin in the 1930s, and beyond. Both aspects of Jacob…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…

Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…

The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…