Substructural Logics A Primer
DOWNLOAD
Download Substructural Logics A Primer PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Substructural Logics A Primer book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Substructural Logics A Primer
DOWNLOAD
Author : F. Paoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-05-31
Substructural Logics A Primer written by F. Paoli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-05-31 with Philosophy categories.
The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.
Substructural Logics A Primer
DOWNLOAD
Author : F. Paoli
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Substructural Logics A Primer written by F. Paoli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Philosophy categories.
Substructural logics are by now one of the most prominent branches of the research field usually labelled as "nonclassical logics" - and perhaps of logic tout court. Over the last few decades a vast amount of research papers and even some books have been devoted to this subject. The aim of the present book is to give a comprehensive account of the "state of the art" of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational). Readership: This textbook is designed for a wide readership: graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics with no previous knowledge of the subject (except for a working knowledge of elementary logic) will be gradually introduced into the field starting from its basic foundations; specialists and researchers in the area will find an up-to-date survey of the most important current research topics and problems.
Algebraic Perspectives On Substructural Logics
DOWNLOAD
Author : Davide Fazio
language : en
Publisher: Springer Nature
Release Date : 2020-11-07
Algebraic Perspectives On Substructural Logics written by Davide Fazio and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-07 with Philosophy categories.
This volume presents the state of the art in the algebraic investigation into substructural logics. It features papers from the workshop AsubL (Algebra & Substructural Logics - Take 6). Held at the University of Cagliari, Italy, this event is part of the framework of the Horizon 2020 Project SYSMICS: SYntax meets Semantics: Methods, Interactions, and Connections in Substructural logics. Substructural logics are usually formulated as Gentzen systems that lack one or more structural rules. They have been intensively studied over the past two decades by logicians of various persuasions. These researchers include mathematicians, philosophers, linguists, and computer scientists. Substructural logics are applicable to the mathematical investigation of such processes as resource-conscious reasoning, approximate reasoning, type-theoretical grammar, and other focal notions in computer science. They also apply to epistemology, economics, and linguistics. The recourse to algebraic methods -- or, better, the fecund interplay of algebra and proof theory -- has proved useful in providing a unifying framework for these investigations. The AsubL series of conferences, in particular, has played an important role in these developments. This collection will appeal to students and researchers with an interest in substructural logics, abstract algebraic logic, residuated lattices, proof theory, universal algebra, and logical semantics.
Residuated Lattices An Algebraic Glimpse At Substructural Logics
DOWNLOAD
Author : Nikolaos Galatos
language : en
Publisher: Elsevier
Release Date : 2007-04-25
Residuated Lattices An Algebraic Glimpse At Substructural Logics written by Nikolaos Galatos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-25 with Mathematics categories.
The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.
An Introduction To Substructural Logics
DOWNLOAD
Author : Greg Restall
language : en
Publisher: Routledge
Release Date : 2002-09-11
An Introduction To Substructural Logics written by Greg Restall and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-11 with Philosophy categories.
This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. An Introduction to Substrucural Logics is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda Both students and professors of philosophy, computing, linguistics, and mathematics will find this to be an important addition to their reading.
Trends In Logic
DOWNLOAD
Author : Vincent F. Hendricks
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Trends In Logic written by Vincent F. Hendricks and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Residuated Structures In Algebra And Logic
DOWNLOAD
Author : George Metcalfe
language : en
Publisher: American Mathematical Society
Release Date : 2023-11-06
Residuated Structures In Algebra And Logic written by George Metcalfe and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-06 with Mathematics categories.
This book is an introduction to residuated structures, viewed as a common thread binding together algebra and logic. The framework includes well-studied structures from classical abstract algebra such as lattice-ordered groups and ideals of rings, as well as structures serving as algebraic semantics for substructural and other non-classical logics. Crucially, classes of these structures are studied both algebraically, yielding a rich structure theory along the lines of Conrad's program for lattice-ordered groups, and algorithmically, via analytic sequent or hypersequent calculi. These perspectives are related using a natural notion of equivalence for consequence relations that provides a bridge offering benefits to both sides. Algorithmic methods are used to establish properties like decidability, amalgamation, and generation by subclasses, while new insights into logical systems are obtained by studying associated classes of structures. The book is designed to serve the purposes of novices and experts alike. The first three chapters provide a gentle introduction to the subject, while subsequent chapters provide a state-of-the-art account of recent developments in the field.
Relevant Logic
DOWNLOAD
Author : Edwin D. Mares
language : en
Publisher: Cambridge University Press
Release Date : 2004-02-26
Relevant Logic written by Edwin D. Mares and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-26 with Philosophy categories.
This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book ends by examining various applications of relevant logic and presenting some interesting open problems.
New Directions In Relevant Logic
DOWNLOAD
Author : Igor Sedlár
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
New Directions In Relevant Logic written by Igor Sedlár and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Philosophy categories.
This book brings together contemporary work on relevant logics to showcase the recent progress of the field and set the stage for future research. The papers in the volume contribute to the formal and philosophical development of the field. They include contributions from different traditions and approaches ranging from philosophical discussions of the foundations of relevant, and related kinds of non-classical, logic to mathematical work concerning open technical problems in the field. This is the first edited collection on the topic in many years, and it includes contributions from established figures as well as younger generations of researchers. Relevant logics have recently seen a resurgence of interest and this volume will be an important resource for logicians working on substructural and relevant logics for years to come.
Pluralisms In Truth And Logic
DOWNLOAD
Author : Jeremy Wyatt
language : en
Publisher: Springer
Release Date : 2018-12-29
Pluralisms In Truth And Logic written by Jeremy Wyatt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-29 with Philosophy categories.
This edited volume brings together 18 state-of-the art essays on pluralism about truth and logic. Parts I and II are dedicated to respectively truth pluralism and logical pluralism, and Part III to their interconnections. Some contributors challenge pluralism, arguing that the nature of truth or logic is uniform. The majority of contributors, however, defend pluralism, articulate novel versions of the view, or contribute to fundamental debates internal to the pluralist camp. The volume will be of interest to truth theorists and philosophers of logic, as well as philosophers interested in relativism, contextualism, metaphysics, philosophy of language, semantics, paradox, epistemology, or normativity.