Related papers: On Constructive Axiomatic Method
We study the general problem of strengthening the logic of a given (partial) (non-deterministic) matrix with a set of axioms, using the idea of rexpansion. We obtain two characterization methods: a very general but not very effective one,…
We show how to build models of Synthetic Algebraic Geometry over rings k such that finitely presented k-algebra have a decidable equality. The construction is done in a constructive and weak (same proof theoretic strength as dependent type…
We present a methodological framework aiming at the support of HCI practitioners and researchers in selecting and applying the most appropriate combination of HCI methods for particular problems. We highlight the need for a clear and…
Reproducibility is a confused terminology. In this paper, I take a fundamental view on reproducibility rooted in the scientific method. The scientific method is analysed and characterised in order to develop the terminology required to…
In this report, I provide a brief summary of the literature in philosophy, psychology and cognitive science about Explanatory Virtues, and link these concepts to eXplainable AI.
Research at the interface between cognitive psychology, neuroscience, and the science of complex, dynamical systems, is piecing together an understanding of the creative process, including how it works, how it can be fostered, and the…
There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Human experts write summaries using different techniques, including extracting a sentence from the document and rewriting it, or fusing various information from the document to abstract it. These techniques are flexible and thus difficult…
The concept of (auto)catalytic systems has become a cornerstone in understanding evolutionary processes in various fields. The common ground is the observation that for the production of new species/goods/ideas/elements etc. the…
The AHP/ANP are multicriteria decision-making theories that deal with both hierarchic structures when the criteria are independent of the alternatives and with networks when there is any dependence within and between elements of the…
This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
This manuscript contains an outline of lectures course "Evolutionary Algorithms" read by the author. The course covers Canonic Genetic Algorithm and various other genetic algorithms as well as evolutionary strategies, genetic programming,…
We have found a "non-purely-constructive" method of acquiring algebraic cycles involving multiple steps. This note tries to present the main idea in the last step by concentrating on an example of 4-folds. The method demonstrates a contrast…
The aim of this paper is to review the use of GenAI in scientometrics, and to begin a debate on the broader implications for the field. First, we provide an introduction on GenAI's generative and probabilistic nature as rooted in…
The statistical methods derived and described in this thesis provide new ways to elucidate the structural properties of text and other symbolic sequences. Generically, these methods allow detection of a difference in the frequency of a…
This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially ZF (Zermelo-Fraenkel set theory).
How should my own decisions affect my beliefs about the outcomes I expect to achieve? If taking a certain action makes me view myself as a certain type of person, it might affect how I think others view me, and how I view others who are…