Related papers: Algorithm and abstraction in formal mathematics
At its core, abstraction is the process of generalizing from specific instances to broader concepts or models, with the primary objective of reducing complexity while preserving properties essential to the intended purpose. It is…
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
We envision a machine capable of solving mathematical problems. Dividing the quantitative reasoning system into two parts: thought processes and cognitive processes, we provide probabilistic descriptions of the architecture.
Formal mathematics is mathematics done within the framework of a formal logic. It offers major benefits to mathematicians as well as to computing professionals, engineers, and scientists who use mathematics in their work. The standard…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be "correct", in the sense of formalizable in a formal proof system. We then present a view on the relationship between…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
In this paper, we analyze axiomatic issues of unconventional computations from a methodological and philosophical point of view. We explain how the new models of algorithms changed the algorithmic universe, making it open and allowing…
We speak of a \textit{computational law} when that law is intended to be enforced by software through an automated decision-making process. As digital technologies evolve to offer more solutions for public administrations, we see an…
The rise of advanced computational algorithms has opened new avenues for computationally intensive research approaches to theory development. However, the opacity of these algorithms and lack of transparency and rigour in their application…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
These are notes on discrete mathematics for computer scientists. The presentation is somewhat unconventional. Indeed I begin with a discussion of the basic rules of mathematical reasoning and of the notion of proof formalized in a natural…
Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…
Despite significant advancements in the conception of (formal) integrated development environments, applying formal methods in software industry is still perceived as a difficult task. To make the task easier, providing tools that help…
Modelling qualitative uncertainty in formal argumentation is essential both for practical applications and theoretical understanding. Yet, most of the existing works focus on \textit{abstract} models for arguing with uncertainty. Following…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we…
Several different ways exist for approaching hard optimization problems. Mathematical programming techniques, including (integer) linear programming-based methods and metaheuristic approaches, are two highly successful streams for…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…