Search

A major hypothesis about conditionals is the Equation in which the probability of a conditional equals the corresponding conditional probability: p(if A then C) = p(C|A). Probabilistic theories often treat it as axiomatic, whereas it follows from the meanings of conditionals in the theory of mental models. In this theory, intuitive models (system 1) do not represent what is false, and so produce errors in estimates of p(if A then C), yielding instead p(A & C). Deliberative models (system 2) are normative, and yield the proportion of cases of A in which C holds, i.e., the Equation. Intuitive estimates of the probability of a conditional about unique events: If covid-19 disappears in the USA, then Biden will run for a second term, together with those of each of its clauses, are liable to yield joint probability distributions that sum to over 100%. The error, which is inconsistent with the probability calculus, is massive when participants estimate the joint probabilities of conditionals with each of the different possibilities to which they refer. This result and others under review corroborate the model theory. [ABSTRACT FROM AUTHOR]

The model of optimum three-dimensional likelihood quantization of the determined or casual volume space is offered by set of equal quanta at which the probability of representation quantized reaches spaces of the maximum value. The size of optimum quantum is defined by distribution of its zone of influence, values of boundary probability and influence parameter. The model of estimation of quantity of the information or other product in quantization space is entered. [ABSTRACT FROM AUTHOR]

Abstract: A large part of the mathematical formalism of quantum mechanics including the probability density, probability density current, uncertainty relations, wave function, momentum operator, kinetic energy, commutation relations and potentials is related to the probabilistic character of quantum measurements. Equations of motion of quantum mechanics can be obtained from the relativistic invariance of the space–time Fisher information. Some properties of potentials and existence of antiparticles are related to the CPT symmetry. Operators representing parallel or serial physical events in experimental setups can be represented by the sum or product of the corresponding operators. [Copyright &y& Elsevier]

Abstract: The curious correlations between distant events in quantum phenomena suggest the existence of non-local influences. Indeed, as John Bell demonstrated in his celebrated theorem, granted some plausible premises any quantum theory will predict the existence of such non-local influences. One of the theorem''s premises is that the probability distribution of states that systems may assume is independent of the measurements that they undergo at a later time. Retro-causal interpretations of quantum mechanics postulate backward influences from measurement events to the state of systems at an earlier time, and accordingly violate this premise. We argue that retro-causal interpretations predict the existence of closed causal loops, which pose challenges for the predictive and explanatory power of these interpretations. [Copyright &y& Elsevier]

Abstract: Popper''s introduction of “propensity” was intended to provide a solid conceptual foundation for objective single-case probabilities. By considering the partly opposed contributions of Humphreys and Miller and Salmon, it is argued that when properly understood, propensities can in fact be understood as objective single-case causal probabilities of transitions between concrete events. The chief claim is that propensities are well-explicated by describing how they fit into the existing formal theory of branching space-times, which is simultaneously indeterministic and causal. Several problematic examples, some commonsense and some quantum-mechanical, are used to make clear the advantages of invoking branching space-times theory in coming to understand propensities. [Copyright &y& Elsevier]

We examine theoretically the dynamic inflation and finite amplitude oscillatory motion of inhomogeneous spherical shells and cylindrical tubes of stochastic hyperelastic material. These bodies are deformed by radially symmetric uniform inflation, and are subjected to either a surface dead load or an impulse traction, uniformly applied in the radial direction. We consider composite shells and tubes with two concentric stochastic homogeneous neo-Hookean phases, and inhomogeneous bodies of stochastic neo-Hookean material with constitutive parameters varying continuously in the radial direction. For the homogeneous materials, we define the elastic parameters as spatially-independent random variables, while for the radially inhomogeneous bodies, we take the parameters as spatially-dependent random fields, described by non-Gaussian probability density functions. Under radially symmetric dynamic deformation treated as quasi-equilibrated motion, we show that the bodies oscillate, i.e., the radius increases up to a point, then decreases, then increases again, and so on, and the amplitude and period of the oscillations are characterised by probability distributions, depending on the initial conditions, the geometry, and the probabilistic material properties. • We study large strain deformations of stochastic isotropic hyperelastic bodies. • Radially inhomogeneous cylindrical tubes and spherical shells are considered. • Dynamic inflation and finite amplitude oscillatory motions are treated explicitly. • The material parameters are defined by non-Gaussian probability densities. • Our probabilistic results demonstrate the nonlinear propagation of uncertainties. [ABSTRACT FROM AUTHOR]