Related papers: On Constructive Axiomatic Method
This paper makes a number of connections between life and various facets of genetic and evolutionary algorithms research. Specifically, it addresses the topics of adaptation, multiobjective optimization, decision making, deception, and…
An overview of the accomplishments of constructive quantum field theory is provided.
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
The nature of the scientific method is controversial with claims that a single scientific method does not even exist. However the scientific method does exist. It is the building of logical and self consistent models to describe nature. The…
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…
Extractive keyphrase generation research has been around since the nineties, but the more advanced abstractive approach based on the encoder-decoder framework and sequence-to-sequence learning has been explored only recently. In fact, more…
Deep learning-based AI models have been extensively applied in genomics, achieving remarkable success across diverse applications. As these models gain prominence, there exists an urgent need for interpretability methods to establish…
In recent years, the study of artificial intelligence (AI) has undergone a paradigm shift. This has been propelled by the groundbreaking capabilities of generative models both in supervised and unsupervised learning scenarios. Generative AI…
The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.
Recent advancements in generative artificial intelligence (generative AI) technologies have transformed the computer science discipline of natural language processing. However, generative AI retains the anthropomorphic model of simulating…
This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…
Generative Artificial Intelligence is emerging as an important technology, promising to be transformative in many areas. At the same time, generative AI techniques are based on sampling from probabilistic models, and by default, they come…
This book brings new mathematical rigour to the ongoing vigorous debate on how to quantify biological diversity. The question "what is diversity?" has surprising mathematical depth, and breadth too: this book involves parts of mathematics…
In this essay, we provide an overview of methodological considerations necessary to lay out the foundation for our PhD research on uncertainty and risk-aware adaptation.
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically…
A short review of the recent results and models of complex networks.
The previous work on controllable text generation is organized using a new schema we provide in this study. Seven components make up the schema, and each one is crucial to the creation process. To accomplish controlled generation for…