Related papers: On the Limits of Experimental Knowledge
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…
The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the…
Background: Many published machine learning studies are irreproducible. Issues with methodology and not properly accounting for variation introduced by the algorithm themselves or their implementations are attributed as the main…
The sensitivities revealed by a sensitivity analysis of a probabilistic network typically depend on the entered evidence. For a real-life network therefore, the analysis is performed a number of times, with different evidence. Although…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
With the relentless rise of computer power, there is a widespread expectation that computers can solve the most pressing problems of science, and even more besides. We explore the limits of computational modelling and conclude that, in the…
When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…
Large-scale datasets are increasingly being used to inform decision making. While this effort aims to ground policy in real-world evidence, challenges have arisen as selection bias and other forms of distribution shifts often plague…
The paper gives a few examples of the phenomena that will never be understood by the mankind. The first example is the physics at the scales of $\sim 10^{-33}$ cm where the gravitation interaction becomes strong, sales at the very beginning…
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],…
In simple perceptual decisions the brain has to identify a stimulus based on noisy sensory samples from the stimulus. Basic statistical considerations state that the reliability of the stimulus information, i.e., the amount of noise in the…
Learned systems in the domain of visual recognition and cognition impress in part because even though they are trained with datasets many orders of magnitude smaller than the full population of possible images, they exhibit sufficient…
Thought experiments involving thermodynamic principles have often been used to derive fundamental physical limits to information processing and storage. Similar thought experiments involving black holes can shed further light into such…
The completeness of quantum mechanics in predictive power is a central question in its foundational study. While most investigations focus on two-dimensional systems, high-dimensional systems are more general and widely applicable. Building…
Access to external knowledge sources through localized knowledge spillovers is an important determinant of the innovative capabilities of firms. However, the geographical extent of knowledge spillovers is not well understood. In this…
Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities---this is the conjunction fallacy. One of the most discussed accounts of this…
Accepting information as a physical category and ascribing to inanimate matter some spirit (consciousness, intelligence) allows to explain quantum-mechanical phenomena, including delayed-choice and EPR-Bohm-Bell experiments, as well as…
Experiments may not reveal their full import at the time that they are performed. The scientists who perform them usually are testing a specific hypothesis and quite often have specific expectations limiting the possible inferences that can…
Although learning from data is effective and has achieved significant milestones, it has many challenges and limitations. Learning from data starts from observations and then proceeds to broader generalizations. This framework is…
Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a…