相关论文: The prospects for mathematical logic in the twenty…

Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…

Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this…

Computers have already changed the way that humans do mathematics: they enable us to compute efficiently. But will they soon be helping us to reason? And will they one day start reasoning themselves? We give an overview of recent…

This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…

The article retraces major events and milestones in the mutual influences between mathematical logic and computer science since the 1950s.

This introduction begins with a section on fundamental notions of mathematical logic, including propositional logic, predicate or first-order logic, completeness, compactness, the L\"owenheim-Skolem theorem, Craig interpolation, Beth's…

This is a reflection on the author's experience in teaching logic at the graduate level in a computer science department. The main lesson is that model building and the process of modelling must be placed at the centre stage of logic…

In the past decade, a lot of progress has been made in the design and evaluation of logic locking; a premier technique to safeguard the integrity of integrated circuits throughout the electronics supply chain. However, the widespread…

In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic…

This is a set of 288 questions written for a Moore-style course in Mathematical Logic. I have used these (or some variation) four times in a beginning graduate course. Topics covered are: propositional logic axioms of ZFC wellorderings and…

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific…

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…

The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…

This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…

Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…

This essay considers ways that recent uses of computers in mathematics challenge contemporary views on the nature of mathematical understanding. It also puts these challenges in a historical perspective and offers speculation as to a…

After a very brief review of twentieth century elementary particle physics, prospects for the next century are discussed. First and most important are technological limits of opportunities; next, the future experimental program, and finally…

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…

Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…

As the etymology of the word shows, logic is intimately related to language, as exemplified by the work of philosophers from Antiquity and from the Middle-Age. At the beginning of the XX century, the crisis of the foundations of mathematics…