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Hiroakira Ono On Substructural Logics
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Book Synopsis Hiroakira Ono on Substructural Logics by : Nikolaos Galatos
Download or read book Hiroakira Ono on Substructural Logics written by Nikolaos Galatos and published by Springer Nature. This book was released on 2021-12-13 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.
Book Synopsis Residuated Lattices: An Algebraic Glimpse at Substructural Logics by : Nikolaos Galatos
Download or read book Residuated Lattices: An Algebraic Glimpse at Substructural Logics written by Nikolaos Galatos and published by Elsevier. This book was released on 2007-04-25 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Proof Theory and Algebra in Logic by : Hiroakira Ono
Download or read book Proof Theory and Algebra in Logic written by Hiroakira Ono and published by Springer. This book was released on 2019-08-02 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part. Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.
Book Synopsis Mathematics, Logic, and their Philosophies by : Mojtaba Mojtahedi
Download or read book Mathematics, Logic, and their Philosophies written by Mojtaba Mojtahedi and published by Springer Nature. This book was released on 2021-02-09 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna’s logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.
Book Synopsis Knowledge, Proof and Dynamics by : Fenrong Liu
Download or read book Knowledge, Proof and Dynamics written by Fenrong Liu and published by Springer. This book was released on 2021-03-24 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers selected papers presented at the Fourth Asian Workshop on Philosophical Logic, held in Beijing in October 2018. The contributions cover a wide variety of topics in modal logic (epistemic logic, temporal logic and dynamic logic), proof theory, algebraic logic, game logics, and philosophical foundations of logic. They also reflect the interdisciplinary nature of logic – a subject that has been studied in fields as diverse as philosophy, linguistics, mathematics, computer science and artificial intelligence. More specifically. The book also presents the latest developments in logic both in Asia and beyond.
Book Synopsis Quantifiers, Propositions and Identity by : Robert Goldblatt
Download or read book Quantifiers, Propositions and Identity written by Robert Goldblatt and published by Cambridge University Press. This book was released on 2011-07-14 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops new semantical characterisations of many logical systems with quantification that are incomplete under the traditional Kripkean possible worlds interpretation. This book is for mathematical or philosophical logicians, computer scientists and linguists, including academic researchers, teachers and advanced students.
Book Synopsis Trends in Logic by : Vincent F. Hendricks
Download or read book Trends in Logic written by Vincent F. Hendricks and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Logic and Implication by : Petr Cintula
Download or read book Logic and Implication written by Petr Cintula and published by Springer Nature. This book was released on 2022-01-01 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.
Book Synopsis Norwegian Runes and Runic Inscriptions by : Terje Spurkland
Download or read book Norwegian Runes and Runic Inscriptions written by Terje Spurkland and published by Boydell Press. This book was released on 2005 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents an accessible account of the Norwegian examples throughout the period of their use. The runic inscriptions are discussed not only from a linguistic point of view but also as sources of information on Norwegian history and culture". --BOOKJACKET.
Book Synopsis Minds Online by : Michelle D. Miller
Download or read book Minds Online written by Michelle D. Miller and published by Harvard University Press. This book was released on 2014-10-13 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: For the Internet generation, educational technology designed with the brain in mind offers a natural pathway to the pleasures and rewards of deep learning. Drawing on neuroscience and cognitive psychology, Michelle Miller shows how attention, memory, critical thinking, and analytical reasoning can be enhanced through technology-aided approaches.
Book Synopsis Algebraic Perspectives on Substructural Logics by : Davide Fazio
Download or read book Algebraic Perspectives on Substructural Logics written by Davide Fazio and published by Springer Nature. This book was released on 2020-11-07 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Graded Consequence by : Mihir Kumar Chakraborty
Download or read book Theory of Graded Consequence written by Mihir Kumar Chakraborty and published by Springer. This book was released on 2019-07-22 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of graded consequence (GCT) and its mathematical formulation. It also compares the notion of graded consequence with other notions of consequence in fuzzy logics, and discusses possible applications of the theory in approximate reasoning and decision-support systems. One of the main points where this book emphasizes on is that GCT maintains the distinction between the three different levels of languages of a logic, namely object language, metalanguage and metametalanguage, and thus avoids the problem of violation of the principle of use and mention; it also shows, gathering evidences from existing fuzzy logics, that the problem of category mistake may arise as a result of not maintaining distinction between levels.
Book Synopsis An Introduction to Substructural Logics by : Greg Restall
Download or read book An Introduction to Substructural Logics written by Greg Restall and published by Routledge. This book was released on 2002-09-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Forced Baptisms by : Marina Caffiero
Download or read book Forced Baptisms written by Marina Caffiero and published by Univ of California Press. This book was released on 2012 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book makes use of newly available archival sources to reexamine the Roman Catholic Church’s policy, from the sixteenth to nineteenth centuries, of coercing the Jews of Rome into converting to Christianity. Marina Caffiero, one of the first historians permitted access to important archives, sets individual stories of denunciation, betrayal, pleading, and conflict into historical context to highlight the Church’s actions and the Jewish response. Caffiero documents the regularity with which Jews were abducted from the Roman ghetto and pressured to accept baptism. She analyzes why some Jewish men, interested in gaining a business advantage, were more inclined to accept conversion than the women. The book exposes the complexity of relations between the papacy and the Jews, revealing the Church not as a monolithic entity, but as a network of competing institutions, and affirming the Roman Jews as active agents of resistance.
Book Synopsis Logic and Foundations of Mathematics by : Andrea Cantini
Download or read book Logic and Foundations of Mathematics written by Andrea Cantini and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The IOth International Congress of Logic, Methodology and Philosophy of Science, which took place in Florence in August 1995, offered a vivid and comprehensive picture of the present state of research in all directions of Logic and Philosophy of Science. The final program counted 51 invited lectures and around 700 contributed papers, distributed in 15 sections. Following the tradition of previous LMPS-meetings, some authors, whose papers aroused particular interest, were invited to submit their works for publication in a collection of selected contributed papers. Due to the large number of interesting contributions, it was decided to split the collection into two distinct volumes: one covering the areas of Logic, Foundations of Mathematics and Computer Science, the other focusing on the general Philosophy of Science and the Foundations of Physics. As a leading choice criterion for the present volume, we tried to combine papers containing relevant technical results in pure and applied logic with papers devoted to conceptual analyses, deeply rooted in advanced present-day research. After all, we believe this is part of the genuine spirit underlying the whole enterprise of LMPS studies.
Book Synopsis Theories of Types and Proofs by : Takahashi, Masako
Download or read book Theories of Types and Proofs written by Takahashi, Masako and published by . This book was released on 1998-12 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Peter Joseph Schroeder-Heister Publisher :Oxford University Press on Demand ISBN 13 :9780198537779 Total Pages :386 pages Book Rating :4.5/5 (377 download)
Book Synopsis Substructural Logics by : Peter Joseph Schroeder-Heister
Download or read book Substructural Logics written by Peter Joseph Schroeder-Heister and published by Oxford University Press on Demand. This book was released on 1993 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new area of logic and computation is now undergoing rapid development. This has affected the social pattern of research in the area. A new topic may rise very quickly with a significant body of research around it. The community, however, cannot wait the traditional two years for a book to appear. This has given greater importance to thematic collections of papers, centred around a topic and addressing it from several points of view, usually as a result of a workshop, summer school, or just a scientific initiative. Such a collection may not be as coherent as a book by one or two authors yet it is more focused than a collection of key papers on a certain topic. It is best thought of as a thematic collection, a study in the area of logic and computation. The new series Studies in Logic and Computation is intended to provide a home for such thematic collections. Substructural logics are nonclassical logics, which arose in response to problems in foundations of mathematics and logic, theoretical computer science, mathematical linguistics, and category theory. They include intuitionistic logic, relevant logic, BCK logic, linear logic, and Lambek's calculus of syntactic categories. Substructural logics differ from classical logics, and from each other, in their presuppositions about Gentzen's structural rules, although their presuppositions about the deductive role of logical constants are invariant. Substructural logics have been a subject of study for logicians during the last sixty years. Specialists have often worked in isolation, however, largely unaware of the contributions of others. This book brings together new papers by some of the most eminent authorities in these varioustraditions to produce a unified view of substructural logics.
