Related papers: Three Conjectures on Unexpectedeness
Normality, in the colloquial sense, has historically been considered an aspirational trait, synonymous with ideality. The arithmetic average and, by extension, statistics including linear regression coefficients, have often been used to…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Recent years have seen a boom in interest in machine learning systems that can provide a human-understandable rationale for their predictions or decisions. However, exactly what kinds of explanation are truly human-interpretable remains…
Different ensembles of the same density matrix are indistinguishable within the modern Kolmogorov probability measure theory of quantum random phenomena. We find that changing the framework from the Kolmogorov one to a frequentist-inspired…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
The logic of abduction involves a collision between deduction and induction, where empirical surprises violate expectations and scientists innovate to resolve them. Here we reformulate abduction as a social process, occurring not only…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
A fundamental result in psycholinguistics is that less predictable words take a longer time to process. One theoretical explanation for this finding is Surprisal Theory (Hale, 2001; Levy, 2008), which quantifies a word's predictability as…
In this paper the author presents some non-conventional thoughts on the complexity of the Universe and the algorithmic reproducibility of the human brain, essentially sparked off by the notion of algorithmic complexity. We must warn that…
The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach,…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Using the ideas of abstract algebra, we introduce the basic concepts of abstract probability theory that generalize the Kolmogorov's probability theory, possibility theory and other theories that deal with uncertainty. Based on abstract…
One of the most complex systems is the human brain whose formalized functioning is characterized by decision theory. We present a "Quantum Decision Theory" of decision making, based on the mathematical theory of separable Hilbert spaces.…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of…
Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical…
The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…
In this paper I conceptualise a novel approach for capturing coincidences between events that have not necessarily an observed causal relationship. Building on the Transcendental Information Cascades approach I outline a tensor theory of…