Related papers: Mathematical Logic in Computer Science
We use an information-theoretic measure of linguistic similarity to investigate the organization and evolution of scientific fields. An analysis of almost 20M papers from the past three decades reveals that the linguistic similarity is…
This two-parts paper offers a survey of linear logic and ludics, which were introduced by Girard in 1986 and 2001, respectively. Both theories revisit mathematical logic from first principles, with inspiration from and applications to…
Curiously overlooked in physics is its dependence on the transmission of numbers. For example the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical…
The century of complexity has come. The face of science has changed. Surprisingly, when we start asking about the essence of these changes and then critically analyse the answers, the result are mostly discouraging. Most of the answers are…
We introduce computational causal inference as an interdisciplinary field across causal inference, algorithms design and numerical computing. The field aims to develop software specializing in causal inference that can analyze massive…
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity (in power) has become in the past half century a main driver…
A hundred years ago, logic was almost synonymous with foundational studies. The ongoing AI revolution raises many deep foundational problems involving neuroscience, philosophy, computer science, and logic. The goal of the following dialog…
In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.
We begin by discussing the history of quantum logic, dividing it into three eras or lives. The first life has to do with Birkhoff and von Neumann's algebraic approach in the 1930's. The second life has to do with attempt to understand…
This article addresses broad trends in interdisciplinary research in physics where interactions with colleagues in fields such as computer science, ecology, or economics can often be derailed by unintentional clashes of methodologies and…
The computing ecosystem has always had deep impacts on society and technology and profoundly changed our lives in myriads of ways. Despite decades of impressive Moore's Law performance scaling and other growth in the computing ecosystem…
Data science methodologies, which have undergone significant developments recently, provide flexible representational performance and fast computational means to address the challenges faced by traditional scientific methodologies while…
Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural net- works to spreading activation models of semantic mem- ory. Recently, however, a new Network Science has been developed, providing…
$ $[This paper is a (self contained) chapter in a new book, Mathematics and Computation, whose draft is available on my homepage at https://www.math.ias.edu/avi/book ]. We survey some concrete interaction areas between computational…
Computational science and engineering (CSE) has been misunderstood to advance with the construction of enormous computers. To the contrary, the historical record demonstrates that innovations in CSE come from improvements to the mathematics…
Recent developments in computer science and artificial intelligence have also contributed to the legal domain, as revealed by the number and range of related publications and applications. Machine and deep learning models require…
The impact of Machine Learning (ML) algorithms in the age of big data and platform capitalism has not spared scientific research in academia. In this work, we will analyse the use of ML in fundamental physics and its relationship to other…
Social science concerns issues on individuals, relationships, and the whole society. The complexity of research topics in social science makes it the amalgamation of multiple disciplines, such as economics, political science, and sociology,…
In contrast to Computer Science, where the fundamental role of Logic is widely recognized, it plays a practically non-existent role in Information Systems curricula. In this paper we argue that instead of Logic's exclusion from the IS…
Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…