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It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
In this paper we review different expansions for neutrino oscillation probabilities in matter in the context of long-baseline neutrino experiments. We examine the accuracy and computational efficiency of different exact and approximate…
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
Cromwell's rule (also known as the zero priors paradox) refers to the constraint of classical probability theory that if one assigns a prior probability of 0 or 1 to a hypothesis, then the posterior has to be 0 or 1 as well (this is a…
We introduce the completeness problem for Modal Logic and examine its complexity. For a definition of completeness for formulas, given a formula of a modal logic, the completeness problem asks whether the formula is complete for that logic.…
We give some sufficient and necessary conditions on a forcing notion Q for preserving the forcing notion ([omega]^{aleph_0},supseteq^*) is proper. They cover many reasonable forcing notions.
Counterfactuals have been recognized as an effective approach to explain classifier decisions. Nevertheless, they have not yet been considered in the context of clustering. In this work, we propose the use of counterfactuals to explain…
Plausibility is a formalization of exact tests for parametric models and generalizes procedures such as Fisher's exact test. The resulting tests are based on cumulative probabilities of the probability density function and evaluate…
Plausible reasoning concerns situations whose inherent lack of precision is not quantified; that is, there are no degrees or levels of precision, and hence no use of numbers like probabilities. A hopefully comprehensive set of principles…
In his paper on the incompleteness theorems, G\"odel seemed to say that a direct way of constructing a formula that says of itself that it is unprovable might involve a faulty circularity. In this note, it is proved that 'direct'…
Plausibility measures are structures for reasoning in the face of uncertainty that generalize probabilities, unifying them with weaker structures like possibility measures and comparative probability relations. So far, the theory of…
The focal loss has demonstrated its effectiveness in many real-world applications such as object detection and image classification, but its theoretical understanding has been limited so far. In this paper, we first prove that the focal…
We describe Monte Carlo methods for estimating lower envelopes of expectations of real random variables. We prove that the estimation bias is negative and that its absolute value shrinks with increasing sample size. We discuss fairly…
For a bucket test with a single criterion for success and a fixed number of samples or testing period, requiring a $p$-value less than a specified value of $\alpha$ for the success criterion produces statistical confidence at level $1 -…
This paper introduces a framework for incorporating prior information into the design of sequential experiments. These sources may include past experiments, expert opinions, or the experimenter's intuition. We model the problem using a…
The fact that the probability density expression provided by the Klein-Gordon equation can take on negative values is usually seen as an obstacle to formulating a particle interpretation of quantum mechanics. Nevertheless, reconciling this…
Counterfactuals are often described as 'retrospective,' focusing on hypothetical alternatives to a realized past. This description relates to an often implicit assumption about the structure and stability of exogenous variables in the…
After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the…
A rigorous quantum relativistic approach has been used to calculate the relationship between the decay laws of an unstable particle seen from two inertial frames moving with respect to each other. In agreement with experiment, it is found…
In calculations of the probability distribution for the cosmological constant, it has been previously assumed that the a priori probability distribution is essentially constant in the very narrow range that is anthropically allowed. This…