Alternative Logics. Do Sciences Need Them?

Alternative Logics. Do Sciences Need Them?

Author: Paul A. Weingartner

Publisher: Springer Science & Business Media

ISBN: 9783662056790

Category: Computers

Page: 368

View: 954

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected here address the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.

Alternative Logics. Do Sciences Need Them?

Alternative Logics. Do Sciences Need Them?

Author: Paul A. Weingartner

Publisher: Springer

ISBN: 3642073913

Category: Computers

Page: 368

View: 268

Initially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected here address the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.

Alternative Logics. Do Sciences Need Them?

Alternative Logics. Do Sciences Need Them?

Author: Paul Weingartner

Publisher: Springer Science & Business Media

ISBN: 3540407448

Category: Computers

Page: 367

View: 268

The contributions collected here address the question of whether the usage of logic in the sciences requires a deviation from classical mathematical logic. The monograph provides a succinct picture of recent research in alternative logics as they have been developed for applications in the sciences.

The Age of Alternative Logics

The Age of Alternative Logics

Author: Johan van Benthem

Publisher: Springer Science & Business Media

ISBN: 9781402050121

Category: Philosophy

Page: 348

View: 506

In the last century, developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great variety of reasoning tasks in the sciences. This book embodies the multi-dimensional interplay between logic and science, presenting contributions from the world's leading scholars on new trends and possible developments for research.

The Realism-Antirealism Debate in the Age of Alternative Logics

The Realism-Antirealism Debate in the Age of Alternative Logics

Author: Shahid Rahman

Publisher: Springer Science & Business Media

ISBN: 940071923X

Category: Philosophy

Page: 348

View: 414

The relation between logic and knowledge has been at the heart of a lively debate since the 1960s. On the one hand, the epistemic approaches based their formal arguments in the mathematics of Brouwer and intuitionistic logic. Following Michael Dummett, they started to call themselves `antirealists'. Others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. Jaakko Hintikka tried to unify both traditions by means of what is now known as `explicit epistemic logic'. Under this view, epistemic contents are introduced into the object language as operators yielding propositions from propositions, rather than as metalogical constraints on the notion of inference. The Realism-Antirealism debate has thus had three players: classical logicians, intuitionists and explicit epistemic logicians. The editors of the present volume believe that in the age of Alternative Logics, where manifold developments in logic happen at a breathtaking pace, this debate should be revisited. Contributors to this volume happily took on this challenge and responded with new approaches to the debate from both the explicit and the implicit epistemic point of view.

Handbook of Philosophical Logic

Handbook of Philosophical Logic

Author: Dov M. Gabbay

Publisher: Springer

ISBN: 9401088012

Category: Philosophy

Page: 531

View: 449

This volume presents a number of systems of logic which can be considered as alternatives to classical logic. The notion of what counts as an alternative is a somewhat problematic one. There are extreme views on the matter of what is the 'correct' logical system and whether one logical system (e. g. classical logic) can represent (or contain) all the others. The choice of the systems presented in this volume was guided by the following criteria for including a logic as an alternative: (i) the departure from classical logic in accepting or rejecting certain theorems of classical logic following intuitions arising from significant application areas and/or from human reasoning; (ii) the alternative logic is well-established and well-understood mathematically and is widely applied in other disciplines such as mathematics, physics, computer science, philosophy, psychology, or linguistics. A number of other alternatives had to be omitted for the present volume (e. g. recent attempts to formulate so-called 'non-monotonic' reason ing systems). Perhaps these can be included in future extensions of the Handbook of Philosophical Logic. Chapter 1 deals with partial logics, that is, systems where sentences do not always have to be either true or false, and where terms do not always have to denote. These systems are thus, in general, geared towards reasoning in partially specified models. Logics of this type have arisen mainly from philo sophical and linguistic considerations; various applications in theoretical computer science have also been envisaged.

Epistemology, Knowledge and the Impact of Interaction

Epistemology, Knowledge and the Impact of Interaction

Author: Juan Redmond

Publisher: Springer

ISBN: 9783319265063

Category: Philosophy

Page: 554

View: 621

With this volume of the series Logic, Epistemology, and the Unity of Science edited by S. Rahman et al. a challenging dialogue is being continued. The series’ first volume argued that one way to recover the connections between logic, philosophy of sciences, and sciences is to acknowledge the host of alternative logics which are currently being developed. The present volume focuses on four key themes. First of all, several chapters unpack the connection between knowledge and epistemology with particular focus on the notion of knowledge as resulting from interaction. Secondly, new epistemological perspectives on linguistics, the foundations of mathematics and logic, physics, biology and law are a subject of analysis. Thirdly, several chapters are dedicated to a discussion of Constructive Type Theory and more generally of the proof-theoretical notion of meaning.Finally, the book brings together studies on the epistemic role of abduction and argumentation theory, both linked to non-monotonic approaches to the dynamics of knowledge.