Related papers: Reflections on Russell's antinomy

Human communication is based on a variety of inferences that we draw from sentences, often going beyond what is literally said. While there is wide agreement on the basic distinction between entailment, implicature, and presupposition, the…

Based on the structure of Fibonacci sequence, we give a new proof for the irrationality exponents of the Fibonacci real numbers. Moreover, we obtain all the irrationality exponents of the real numbers corresponding to the differences of…

In this paper we look at popular fairness methods that use causal counterfactuals. These methods capture the intuitive notion that a prediction is fair if it coincides with the prediction that would have been made if someone's race, gender…

Any stretching of Ringel's non-Pappus pseudoline arrangement when projected into the Euclidean plane, implicitly contains a particular arrangement of nine triangles. This arrangement has a complex constraint involving the sines of its…

In this paper we present two original methods for recognizing textual inference. First one is a modified resolution method such that some linguistic considerations are introduced in the unification of two atoms. The approach is possible due…

Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…

The study of taxonomies and hypernymy relations has been extensive on the Natural Language Processing (NLP) literature. However, the evaluation of taxonomy learning approaches has been traditionally troublesome, as it mainly relies on…

A new interpretation offers a consistent conceptual basis for nonrelativistic quantum mechanics. The Einstein-Podolsky-Rosen (EPR) paradox is solved and the violation of Bell's inequality is explained by maintaining realism, inductive…

In this paper we give a rigorous proof of the equivalence of some different forms of Faraday's law of induction clarifying some misconceptions on the subject and emphasizing that many derivations of this law appearing in textbooks and…

A simple framework for reasoning under uncertainty and intervention is introduced. This is achieved in three steps. First, logic is restated in set-theoretic terms to obtain a framework for reasoning under certainty. Second, this framework…

We introduce a novel logical notion--partial entailment--to propositional logic. In contrast with classical entailment, that a formula P partially entails another formula Q with respect to a background formula set \Gamma intuitively means…

The aim of this work is to describe the equivalence relations in $\Q/\Z$ that arise as the rational lamination of polynomials with all cycles repelling. We also describe where in parameter space one can find a polynomial with all cycles…

There are three principle paradigms of statistics: Bayesian, frequentist and information-based inference. Although these paradigms are in agreement in some contexts, the Lindley paradox describes a class of problems, models of unknown…

We combine several folklore observations to provide a working framework for iterating constructions which contradict the axiom of choice. We use this to define a model in which any kind of structural failure must fail with a proper class of…

Bell's theorem for systems more complicated than two qubits faces a hidden, as yet undiscussed, problem. One of the methods to derive Bell's inequalities is to assume existence of joint probability distribution for measurement results for…

We propose investigating a summation analog of the paradigm for parallel integration. We make some first steps towards an indefinite summation method applicable to summands that rationally depend on the summation index and a P-recursive…

Machine learning based decision making systems are increasingly affecting humans. An individual can suffer an undesirable outcome under such decision making systems (e.g. denied credit) irrespective of whether the decision is fair or…

Accounting for the epistemic contribution of deduction has been a pervasive problem for logicians interested in deduction, such as, among others, Jakko Hintikka. The problem arises because the conclusion validly deduced from a set of…

It is argued that Marxism, being based on contradictions, is an illogical method. More specifically, we present a rejection of Marx's thesis that the rate of profit has a long-term tendency to fall.

The robust Poisson method is becoming increasingly popular when estimating the association of exposures with a binary outcome. Unlike the logistic regression model, the robust Poisson method yields results that can be interpreted as risk or…