Proof, Logic and Formalization
Title | Proof, Logic and Formalization PDF eBook |
Author | Michael Detlefsen |
Publisher | Routledge |
Pages | 391 |
Release | 2005-07-08 |
Genre | Philosophy |
ISBN | 1134975279 |
The mathematical proof is the most important form of justification in mathematics. It is not, however, the only kind of justification for mathematical propositions. The existence of other forms, some of very significant strength, places a question mark over the prominence given to proof within mathematics. This collection of essays, by leading figures working within the philosophy of mathematics, is a response to the challenge of understanding the nature and role of the proof.
Proof, Logic and Formalization
Title | Proof, Logic and Formalization PDF eBook |
Author | Michael Detlefsen |
Publisher | Routledge |
Pages | 251 |
Release | 2005-07-08 |
Genre | Mathematics |
ISBN | 1134975287 |
A collection of essays from distinguished contributors looking at why it is that mathematical proof is given precedence over other forms of mathematical justification.
Homotopy Type Theory: Univalent Foundations of Mathematics
Title | Homotopy Type Theory: Univalent Foundations of Mathematics PDF eBook |
Author | |
Publisher | Univalent Foundations |
Pages | 484 |
Release | |
Genre | |
ISBN |
Proof and Knowledge in Mathematics
Title | Proof and Knowledge in Mathematics PDF eBook |
Author | Michael Detlefsen |
Publisher | Routledge |
Pages | 410 |
Release | 2005-08-18 |
Genre | Philosophy |
ISBN | 1134916752 |
These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is a priori or a posteriori in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification,
Proofs and Algorithms
Title | Proofs and Algorithms PDF eBook |
Author | Gilles Dowek |
Publisher | Springer Science & Business Media |
Pages | 161 |
Release | 2011-01-11 |
Genre | Computers |
ISBN | 0857291211 |
Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation. Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, Gödel’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself. Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.
A Formalization of Set Theory without Variables
Title | A Formalization of Set Theory without Variables PDF eBook |
Author | Alfred Tarski |
Publisher | American Mathematical Soc. |
Pages | 342 |
Release | 1987 |
Genre | Mathematics |
ISBN | 0821810413 |
Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.
Isabelle
Title | Isabelle PDF eBook |
Author | Lawrence C. Paulson |
Publisher | Springer Science & Business Media |
Pages | 348 |
Release | 1994-07-28 |
Genre | Computers |
ISBN | 9783540582441 |
This volume presents the proceedings of the First International Static Analysis Symposium (SAS '94), held in Namur, Belgium in September 1994. The proceedings comprise 25 full refereed papers selected from 70 submissions as well as four invited contributions by Charles Consel, Saumya K. Debray, Thomas W. Getzinger, and Nicolas Halbwachs. The papers address static analysis aspects for various programming paradigms and cover the following topics: generic algorithms for fixpoint computations; program optimization, transformation and verification; strictness-related analyses; type-based analyses and type inference; dependency analyses and abstract domain construction.