Proof-net Categories
Author | : Kosta Dosen |
Publisher | : Polimetrica s.a.s. |
Total Pages | : 155 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 8876990801 |
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Author | : Kosta Dosen |
Publisher | : Polimetrica s.a.s. |
Total Pages | : 155 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 8876990801 |
Author | : Dieter Probst |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 392 |
Release | : 2016-07-25 |
Genre | : Philosophy |
ISBN | : 1501502646 |
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.
Author | : Helmut Schwichtenberg |
Publisher | : Springer Science & Business Media |
Total Pages | : 419 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 9401004137 |
As society comes to rely increasingly on software for its welfare and prosperity there is an urgent need to create systems in which it can trust. Experience has shown that confidence can only come from a more profound understanding of the issues, which in turn can come only if it is based on logically sound foundations. This volume contains contributions from leading researchers in the critical disciplines of computing and information science, mathematics, logic, and complexity. All contributions are self-contained, aiming at comprehensibility as well as comprehensiveness. The volume also contains introductory hints to technical issues, concise surveys, introductions, and various fresh results and new perspectives.
Author | : Thomas Piecha |
Publisher | : Springer |
Total Pages | : 281 |
Release | : 2015-10-24 |
Genre | : Philosophy |
ISBN | : 331922686X |
This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning, and the defence of model theory. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers, and mathematicians alike.
Author | : Juliette Kennedy |
Publisher | : Springer |
Total Pages | : 411 |
Release | : 2017-07-10 |
Genre | : Mathematics |
ISBN | : 3662553864 |
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.
Author | : Stefano Berardi |
Publisher | : Springer |
Total Pages | : 331 |
Release | : 2009-06-07 |
Genre | : Computers |
ISBN | : 3642024440 |
These proceedings contain a selection of refereed papers presented at or - lated to the Annual Workshop of the TYPES project (EU coordination action 510996), which was held during March 26–29, 2008 in Turin, Italy. The topic of this workshop, and of all previous workshops of the same project, was f- mal reasoning and computer programming based on type theory: languages and computerized tools for reasoning, and applications in several domains such as analysis of programming languages, certi?ed software, mobile code, formali- tion of mathematics, mathematics education. The workshop was attended by more than 100 researchers and included more than 40 presentations. We also had three invited lectures, from A. Asperti (University of Bologna), G. Dowek (LIX, Ecole polytechnique, France) and J. W. Klop (Vrije Universiteit, A- terdam, The Netherlands). From 27 submitted papers, 19 were selected after a reviewing process. Each submitted paper was reviewed by three referees; the ?nal decisions were made by the editors. This workshop is the last of a series of meetings of the TYPES working group funded by the European Union (IST project 29001, ESPRIT Working Group 21900, ESPRIT BRA 6435).
Author | : Heinrich Wansing |
Publisher | : Springer |
Total Pages | : 469 |
Release | : 2014-11-27 |
Genre | : Philosophy |
ISBN | : 3319110411 |
This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.
Author | : Roussanka Loukanova |
Publisher | : Springer Nature |
Total Pages | : 205 |
Release | : 2019-09-30 |
Genre | : Technology & Engineering |
ISBN | : 3030300773 |
This book focuses mainly on logical approaches to computational linguistics, but also discusses integrations with other approaches, presenting both classic and newly emerging theories and applications.Decades of research on theoretical work and practical applications have demonstrated that computational linguistics is a distinctively interdisciplinary area. There is convincing evidence that computational approaches to linguistics can benefit from research on the nature of human language, including from the perspective of its evolution. This book addresses various topics in computational theories of human language, covering grammar, syntax, and semantics. The common thread running through the research presented is the role of computer science, mathematical logic and other subjects of mathematics in computational linguistics and natural language processing (NLP). Promoting intelligent approaches to artificial intelligence (AI) and NLP, the book is intended for researchers and graduate students in the field.
Author | : |
Publisher | : |
Total Pages | : 648 |
Release | : 2008 |
Genre | : Logic, Symbolic and mathematical |
ISBN | : |
Author | : Kurt Engesser |
Publisher | : Elsevier |
Total Pages | : 727 |
Release | : 2009-06-16 |
Genre | : Mathematics |
ISBN | : 0080931669 |
Quantum mechanics is said to be the most successful physical theory ever. It is, in fact, unique in its success when applied to concrete physical problems. On the other hand, however, it raises profound conceptual problems that are equally unprecedented. Quantum logic, the topic of this volume, can be described as an attempt to cast light on the puzzle of quantum mechanics from the point of view of logic. Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled, “The logic of quantum mechanics, quantum logic has undergone an enormous development. Various schools of thought and approaches have emerged, and there are a variety of technical results. The chapters of this volume constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic. Authored by eminent scholars in the field Material presented is of recent origin representing the frontier of the subject Provides the most comprehensive and varied discussion of Quantum Mechanics available