Related papers: Facticity as the amount of self-descriptive inform…
String theory has not even come close to a complete formulation after half a century of intense research. On the other hand, a number of features of the theory suggest that the theory, once completed, may be a final theory. It is argued in…
The average uncertainty associated with words is an information-theoretic concept at the heart of quantitative and computational linguistics. The entropy has been established as a measure of this average uncertainty - also called average…
Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program…
Despite the lack of experimental confirmation and of unambiguous theoretical proof, superstring theory has long been considered by many the only consistent quantized theory of gravity and the unique viable framework for the unification of…
Long-form factuality evaluation assesses the ability of models to generate accurate, comprehensive responses to short prompts. Existing benchmarks often lack human verification, leading to potential quality issues. To address this…
We present FAKTA which is a unified framework that integrates various components of a fact checking process: document retrieval from media sources with various types of reliability, stance detection of documents with respect to given…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
String complexity is defined as the cardinality of a set of all distinct words (factors) of a given string. For two strings, we introduce the joint string complexity as the cardinality of a set of words that are common to both strings.…
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two…
The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…
We initiate an investigation how the fundamental concept of independence can be represented effectively in the presence of incomplete information in relational databases. The concepts of possible and certain independence are proposed, and…
Network or graph structures are ubiquitous in the study of complex systems. Often, we are interested in complexity trends of these system as it evolves under some dynamic. An example might be looking at the complexity of a food web as…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
Complexity theory offers a variety of concise computational models for computing boolean functions - branching programs, circuits, decision trees and ordered binary decision diagrams to name a few. A natural question that arises in this…
Traditional fact checking by expert journalists cannot keep up with the enormous volume of information that is now generated online. Computational fact checking may significantly enhance our ability to evaluate the veracity of dubious…
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a…
It is not obvious what fraction of all the potential information residing in the molecules and structures of living systems is significant or meaningful to the system. Sets of random sequences or identically repeated sequences, for example,…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
Despite recent improvements in abstractive summarization, most current approaches generate summaries that are not factually consistent with the source document, severely restricting their trust and usage in real-world applications. Recent…
We propose an axiomatic foundation of mathematics based on the finite sequence as the foundational concept, rather than based on logic and set, as in set theory, or based on type as in dependent type theories. Finite sequences lead to a…