Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations
Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations

Author: Gemma Robles

Publisher: Academic Press

Published: 2018-01-02

Total Pages: 160

ISBN-13: 0128045094

DOWNLOAD EBOOK

Routley-Meyer Ternary Relational Semantics for Intuitionistic-type Negations examines how to introduce intuitionistic-type negations into RM-semantics. RM-semantics is highly malleable and capable of modeling families of logics which are very different from each other. This semantics was introduced in the early 1970s, and was devised for interpreting relevance logics. In RM-semantics, negation is interpreted by means of the Routley operator, which has been almost exclusively used for modeling De Morgan negations. This book provides research on particular features of intuitionistic-type of negations in RM-semantics, while also defining the basic systems and many of their extensions by using models with or without a set of designated points. - Provides a clear development of the fundamentals of RM-semantics in a new application - Covers the most general research on ternary relational semantics - Includes scrutiny of constructive negation from the ternary relational perspective

Relevance Logic
Relevance Logic

Author: Shay Allen Logan

Publisher: Cambridge University Press

Published: 2024-04-30

Total Pages: 102

ISBN-13: 1009227785

DOWNLOAD EBOOK

Relevance logics are a misunderstood lot. Despite being the subject of intense study for nearly a century, they remain maligned as too complicated, too abstruse, or too silly to be worth learning much about. This Element aims to dispel these misunderstandings. By focusing on the weak relevant logic B, the discussion provides an entry point into a rich and diverse family of logics. Also, it contains the first-ever textbook treatment of quantification in relevance logics, as well as an overview of the cutting edge on variable sharing results and a guide to further topics in the field.

What is Negation?
What is Negation?

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

Published: 1999-03-31

Total Pages: 352

ISBN-13: 9780792355694

DOWNLOAD EBOOK

The properties of negation, in combination with those of other logical operations and structural features of the deductibility relation, serve as gateways among logical systems. Negation therefore plays an important role in selecting logical systems for particular applications. This volume provides a thorough treatment of this concept, based on contributions written by authors from various branches of logic. The resulting 14 research papers address a variety of topics including negation in relevant logics; a defense of dialetheic theory of negation; stable negation in logic programming; antirealism and falsity; and negation, denial, and language change in philosophical logic. Suited to scholars and graduate students in the fields of philosophy, logic mathematics, computer science, and linguistics. Annotation copyrighted by Book News, Inc., Portland, OR

Goal-Directed Proof Theory
Goal-Directed Proof Theory

Author: Dov M. Gabbay

Publisher: Springer Science & Business Media

Published: 2000-08-31

Total Pages: 282

ISBN-13: 9780792364733

DOWNLOAD EBOOK

Goal Directed Proof Theory presents a uniform and coherent methodology for automated deduction in non-classical logics, the relevance of which to computer science is now widely acknowledged. The methodology is based on goal-directed provability. It is a generalization of the logic programming style of deduction, and it is particularly favourable for proof search. The methodology is applied for the first time in a uniform way to a wide range of non-classical systems, covering intuitionistic, intermediate, modal and substructural logics. The book can also be used as an introduction to these logical systems form a procedural perspective. Readership: Computer scientists, mathematicians and philosophers, and anyone interested in the automation of reasoning based on non-classical logics. The book is suitable for self study, its only prerequisite being some elementary knowledge of logic and proof theory.

Impossible Worlds
Impossible Worlds

Author: Francesco Berto

Publisher: Oxford University Press

Published: 2019

Total Pages: 333

ISBN-13: 0198812795

DOWNLOAD EBOOK

The latter half of the 20 ...

Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs
Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs

Author: Ivo Düntsch

Publisher: Springer Nature

Published: 2021-09-24

Total Pages: 591

ISBN-13: 3030714306

DOWNLOAD EBOOK

This book is dedicated to the work of Alasdair Urquhart. The book starts out with an introduction to and an overview of Urquhart’s work, and an autobiographical essay by Urquhart. This introductory section is followed by papers on algebraic logic and lattice theory, papers on the complexity of proofs, and papers on philosophical logic and history of logic. The final section of the book contains a response to the papers by Urquhart. Alasdair Urquhart has made extremely important contributions to a variety of fields in logic. He produced some of the earliest work on the semantics of relevant logic. He provided the undecidability of the logics R (of relevant implication) and E (of relevant entailment), as well as some of their close neighbors. He proved that interpolation fails in some of those systems. Urquhart has done very important work in complexity theory, both about the complexity of proofs in classical and some nonclassical logics. In pure algebra, he has produced a representation theorem for lattices and some rather beautiful duality theorems. In addition, he has done important work in the history of logic, especially on Bertrand Russell, including editing Volume four of Russell’s Collected Papers.