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Author: Katalin Bimbó Publisher: Center for the Study of Language and Information Publica Tion ISBN: Category : Language Arts & Disciplines Languages : en Pages : 400
Book Description
Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
Author: Katalin Bimbó Publisher: Center for the Study of Language and Information Publica Tion ISBN: Category : Language Arts & Disciplines Languages : en Pages : 400
Book Description
Nonclassical logics have played an increasing role in recent years in disciplines ranging from mathematics and computer science to linguistics and philosophy. Generalized Galois Logics develops a uniform framework of relational semantics to mediate between logical calculi and their semantics through algebra. This volume addresses normal modal logics such as K and S5, and substructural logics, including relevance logics, linear logic, and Lambek calculi. The authors also treat less-familiar and new logical systems with equal deftness.
Author: J. Michael Dunn Publisher: ISBN: 9781848903180 Category : Mathematics Languages : en Pages : 144
Book Description
J. Michael Dunn's PhD dissertation occupies a unique place in the development of the algebraic approach to logic. In The Algebra of Intensional Logics, Dunn introduced De Morgan monoids, a class of algebras in which the algebra of R (the logic of relevant implication) is free. This is an example where a logic's algebra is neither a Boolean algebra with further operations, nor a residuated distributive lattice. De Morgan monoids served as a paradigm example for the algebraization of other relevance logics, including E, the logic of entailment and R-Mingle (RM), the extension of R with the mingle axiom. De Morgan monoids extend De Morgan lattices, which algebraize the logic of first-degree entailments that is a common fragment of R and E. Dunn studied the role of the four-element De Morgan algebra D in the representation of De Morgan lattices, and from this he derived a completeness theorem for first-degree entailments. He also showed that every De Morgan lattice can be embedded into a 2-product of Boolean algebras, and proved related results about De Morgan lattices in which negation has no fixed point. Dunn also developed an informal interpretation for first-degree entailments utilizing the notion of aboutness, which was motivated by the representation of De Morgan lattices by sets. Dunn made preeminent contributions to several areas of relevance logic in his career spanning more than half a century. In proof theory, he developed sequent calculuses for positive relevance logics and a tableaux system for first-degree entailments; in semantics, he developed a binary relational semantics for the logic RM. The use of algebras remained a central theme in Dunn's work from the proof of the admissibility of the rule called γ to his theory of generalized Galois logics (or ``gaggles''), in which the residuals of arbitrary operations are considered. The representation of gaggles---utilizing relational structures---gave a new framework for relational semantics for relevance and for so-called substructural logics, and led to an information-based interpretation of them.
Author: Katalin Bimbo Publisher: CRC Press ISBN: 1466564687 Category : Mathematics Languages : en Pages : 386
Book Description
Although sequent calculi constitute an important category of proof systems, they are not as well known as axiomatic and natural deduction systems. Addressing this deficiency, Proof Theory: Sequent Calculi and Related Formalisms presents a comprehensive treatment of sequent calculi, including a wide range of variations. It focuses on sequent calculi
Author: Katalin Bimbo Publisher: Springer ISBN: 3319293001 Category : Philosophy Languages : en Pages : 469
Book Description
This book celebrates and expands on J. Michael Dunn’s work on informational interpretations of logic. Dunn, in his Ph.D. thesis (1966), introduced a semantics for first-degree entailments utilizing the idea that a sentence can provide positive or negative information about a topic, possibly supplying both or neither. He later published a related interpretation of the logic R-mingle, which turned out to be one of the first relational semantics for a relevance logic. An incompatibility relation between information states lends itself to a definition of negation and it has figured into Dunn's comprehensive investigations into representations of various negations. The informational view of semantics is also a prominent theme in Dunn’s research on other logics, such as quantum logic and linear logic, and led to the encompassing theory of generalized Galois logics (or "gaggles"). Dunn’s latest work addresses informational interpretations of the ternary accessibility relation and the very nature of information. The book opens with Dunn’s autobiography, followed by a list of his publications. It then presents a series of papers written by respected logicians working on different aspects of information-based logics. The topics covered include the logic R-mingle, which was introduced by Dunn, and its applications in mathematical reasoning as well as its importance in obtaining results for other relevance logics. There are also interpretations of the accessibility relation in the semantics of relevance and other non-classical logics using different notions of information. It also presents a collection of papers that develop semantics for various logics, including certain modal and many-valued logics. The publication of this book is well timed, since we are living in an "information age.” Providing new technical findings, intellectual history and careful expositions of intriguing ideas, it appeals to a wide audience of scholars and researchers.
Author: Ofer Arieli Publisher: Springer Nature ISBN: 3030712583 Category : Philosophy Languages : en Pages : 369
Book Description
This book is a collection of contributions honouring Arnon Avron’s seminal work on the semantics and proof theory of non-classical logics. It includes presentations of advanced work by some of the most esteemed scholars working on semantic and proof-theoretical aspects of computer science logic. Topics in this book include frameworks for paraconsistent reasoning, foundations of relevance logics, analysis and characterizations of modal logics and fuzzy logics, hypersequent calculi and their properties, non-deterministic semantics, algebraic structures for many-valued logics, and representations of the mechanization of mathematics. Avron’s foundational and pioneering contributions have been widely acknowledged and adopted by the scientific community. His research interests are very broad, spanning over proof theory, automated reasoning, non-classical logics, foundations of mathematics, and applications of logic in computer science and artificial intelligence. This is clearly reflected by the diversity of topics discussed in the chapters included in this book, all of which directly relate to Avron’s past and present works. This book is of interest to computer scientists and scholars of formal logic.
Author: Christian Ebert Publisher: Springer Science & Business Media ISBN: 3642143210 Category : Computers Languages : en Pages : 305
Book Description
This volume contains a selection of papers presented at the 10th and 11th Meeting of the Association for Mathematics of Language, held in Los Angeles, CA, USA in July 2007 and in Bielefeld, Germany, in August 2009.The 19 revised papers presented together with 3 invited speeches were carefully selected from numerous submissions. The papers in this collection reflect a wide range of theoretical topics relating to language and computation including papers on the intersection of computational complexity, formal language theory, proof theory, and logic, as well as phonology, lexical semantics, syntax and typology.
Author: Katalin Bimbó
Author: Katalin Bimbó
Author: J. Michael Dunn
Author: Eugene Leo Allgower
Author: Katalin Bimbo
Author: Katalin Bimbo
Author: Paul Ponomarenko
Author: Ofer Arieli
Author: Heinrich Wansing
Author: Erwin Engeler
Author: Christian Ebert