Related papers: Facticity as the amount of self-descriptive inform…
A description is an entity that can be interpreted as true or false of an object, and using feature structures as descriptions accrues several computational benefits. In this paper, I create an explicit interpretation of a typed feature…
The tensionless limit of classical string theory may be formulated as a topological theory on the world-sheet. A vector density carries geometrical information in place of an internal metric. It is found that path-integral quantization…
The volume and velocity of information that gets generated online limits current journalistic practices to fact-check claims at the same rate. Computational approaches for fact checking may be the key to help mitigate the risks of massive…
The multiplicative theory of a set of numbers (which could be natural, integer, rational, real or complex numbers) is the first-order theory of the structure of that set with (solely) the multiplication operation (that set is taken to be…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
Formalising the confrontation of opinions (models) to observations (data) is the task of Inferential Statistics. Information Theory provides us with a basic functional, the relative entropy (or Kullback-Leibler divergence), an asymmetrical…
Complex network theory is used to investigate the structure of meaningful concepts in written texts of individual authors. Networks have been constructed after a two phase filtering, where words with less meaning contents are eliminated,…
Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…
Forecasting is usually framed as a problem of model choice. This paper starts earlier, asking how much predictive information is available at each horizon. Under logarithmic loss, the answer is exact: the mutual information between the…
We present a theory of information expressed solely in terms of which transformations of physical systems are possible and which are impossible - i.e. in constructor-theoretic terms. Although it includes conjectured laws of physics that are…
We know extensions of first order logic by quantifiers of the kind "there are uncountable many ...", "most ..." with new axioms and appropriate semantics. Related are operations such as "set of x, such that ...", Hilbert's…
For each partition of a data set into a given number of parts there is a partition such that every part is as much as possible a good model (an "algorithmic sufficient statistic") for the data in that part. Since this can be done for every…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…
During a spontaneous change, a macroscopic physical system will evolve towards a macro-state with more realizations. This observation is at the basis of the Statistical Mechanical version of the Second Law of Thermodynamics, and it provides…
We define {\em predictive information} $I_{\rm pred} (T)$ as the mutual information between the past and the future of a time series. Three qualitatively different behaviors are found in the limit of large observation times $T$: $I_{\rm…
Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent,…
We propose a computational framework to quantify (measure) and to optimize the reliability of complex systems. The approach uses a graph representation of the system that is subject to random failures of its components (nodes and edges).…