Quantification in Nonclassical Logic

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional modal logics, this book is the first detailed monograph in nonclassical first-order quantification. It includes results obtained during the past thirty years. The field is very large, so we confine ourselves with only two kinds of logics: modal and superintuitionistic. The main emphasis of Volume 1 is model-theoretic, and it concentrates on descriptions of different sound semantics and completeness problem --- even for these seemingly simple questions we have our hands full. The major part of the presented material has never been published before. Some results are very recent, and for other results we either give new proofs or first proofs in full detail.

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  • Author : Dov M. Gabbay
  • Publisher : Elsevier
  • Pages : 640 pages
  • ISBN : 008093112X
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKQuantification in Nonclassical Logic

Quantification in Nonclassical Logic

Quantification in Nonclassical Logic
  • Author : Dov M. Gabbay,Dimitrij Skvortsov,Valentin Shehtman
  • Publisher : Elsevier
  • Release : 20 June 2009
GET THIS BOOKQuantification in Nonclassical Logic

Quantification and modalities have always been topics of great interest for logicians. These two themes emerged from philosophy and language in ancient times; they were studied by traditional informal methods until the 20th century. In the last century the tools became highly mathematical, and both modal logic and quantification found numerous applications in Computer Science. At the same time many other kinds of nonclassical logics were investigated and applied to Computer Science. Although there exist several good books in propositional

Labelled Non-Classical Logics

Labelled Non-Classical Logics
  • Author : Luca Viganò
  • Publisher : Springer Science & Business Media
  • Release : 17 April 2013
GET THIS BOOKLabelled Non-Classical Logics

I am very happy to have this opportunity to introduce Luca Vigano's book on Labelled Non-Classical Logics. I put forward the methodology of labelled deductive systems to the participants of Logic Colloquium'90 (Labelled Deductive systems, a Position Paper, In J. Oikkonen and J. Vaananen, editors, Logic Colloquium '90, Volume 2 of Lecture Notes in Logic, pages 66-68, Springer, Berlin, 1993), in an attempt to bring labelling as a recognised and significant component of our logic culture. It was a response to earlier

Structural Analysis of Non-Classical Logics

Structural Analysis of Non-Classical Logics
  • Author : Syraya Chin-Mu Yang,Duen-Min Deng,Hanti Lin
  • Publisher : Springer
  • Release : 16 October 2015
GET THIS BOOKStructural Analysis of Non-Classical Logics

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians to address a diversity of topics on the structural analysis of non-classical logics. It mainly focuses on the construction of different types of models for various non-classical logics of current interest, including modal logics, epistemic logics, dynamic logics, and observational predicate logic. The book presents a wide range of applications of two well-known approaches in current research: (i) structural modeling of certain philosophical issues in the framework

Quantifiers, Propositions and Identity

Quantifiers, Propositions and Identity
  • Author : Robert Goldblatt
  • Publisher : Cambridge University Press
  • Release : 14 July 2011
GET THIS BOOKQuantifiers, Propositions and Identity

Many systems of quantified modal logic cannot be characterised by Kripke's well-known possible worlds semantic analysis. This book shows how they can be characterised by a more general 'admissible semantics', using models in which there is a restriction on which sets of worlds count as propositions. This requires a new interpretation of quantifiers that takes into account the admissibility of propositions. The author sheds new light on the celebrated Barcan Formula, whose role becomes that of legitimising the Kripkean interpretation

Handbook of Modal Logic

Handbook of Modal Logic
  • Author : Patrick Blackburn,Johan F.A.K. van Benthem,Frank Wolter
  • Publisher : Elsevier
  • Release : 03 November 2006
GET THIS BOOKHandbook of Modal Logic

The Handbook of Modal Logic contains 20 articles, which collectively introduce contemporary modal logic, survey current research, and indicate the way in which the field is developing. The articles survey the field from a wide variety of perspectives: the underling theory is explored in depth, modern computational approaches are treated, and six major applications areas of modal logic (in Mathematics, Computer Science, Artificial Intelligence, Linguistics, Game Theory, and Philosophy) are surveyed. The book contains both well-written expository articles, suitable for beginners

Philosophical Logic: Current Trends in Asia

Philosophical Logic: Current Trends in Asia
  • Author : Syraya Chin-Mu Yang,Kok Yong Lee,Hiroakira Ono
  • Publisher : Springer
  • Release : 25 November 2017
GET THIS BOOKPhilosophical Logic: Current Trends in Asia

This volume brings together a group of logic-minded philosophers and philosophically oriented logicians, mainly from Asia, to address a variety of logical and philosophical topics of current interest, offering a representative cross-section of the philosophical logic landscape in early 21st-century Asia. It surveys a variety of fields, including modal logic, epistemic logic, formal semantics, decidability and mereology. The book proposes new approaches and constructs more powerful frameworks, such as cover theory, an algebraic approach to cut-elimination, and a Boolean approach

Leo Esakia on Duality in Modal and Intuitionistic Logics

Leo Esakia on Duality in Modal and Intuitionistic Logics
  • Author : Guram Bezhanishvili
  • Publisher : Springer
  • Release : 03 June 2014
GET THIS BOOKLeo Esakia on Duality in Modal and Intuitionistic Logics

This volume is dedicated to Leo Esakia's contributions to the theory of modal and intuitionistic systems. Consisting of 10 chapters, written by leading experts, this volume discusses Esakia’s original contributions and consequent developments that have helped to shape duality theory for modal and intuitionistic logics and to utilize it to obtain some major results in the area. Beginning with a chapter which explores Esakia duality for S4-algebras, the volume goes on to explore Esakia duality for Heyting algebras and

New Frontiers in Artificial Intelligence

New Frontiers in Artificial Intelligence
  • Author : Yoichi Motomura,Alastair Butler,Daisuke Bekki
  • Publisher : Springer
  • Release : 19 July 2013
GET THIS BOOKNew Frontiers in Artificial Intelligence

This book constitutes the thoroughly refereed post-conference proceedings of the JSAI-isAI 2012 Workshops LENLS, JURISIN, ALSIP, MiMI, which tool place on November/December 2012, respectively, in Miyazaki, Japan. The 17 contributions in this volume were carefully reviewed and selected from 42 submissions.They are an excellent selection of papers that are representative of topics of AI research both in Japan an in other parts of the world. LENLS (Logic and Engineering of Natural Language Semantics) is an annual international workshop on formal semantics and

Hiroakira Ono on Substructural Logics

Hiroakira Ono on Substructural Logics
  • Author : Nikolaos Galatos,Kazushige Terui
  • Publisher : Springer Nature
  • Release : 13 December 2021
GET THIS BOOKHiroakira Ono on Substructural Logics

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),

Neighborhood Semantics for Modal Logic

Neighborhood Semantics for Modal Logic
  • Author : Eric Pacuit
  • Publisher : Springer
  • Release : 15 November 2017
GET THIS BOOKNeighborhood Semantics for Modal Logic

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic (the so-called non-normal modal logics). In addition, the book discusses a broad range of topics, including standard modal logic results (i.e., completeness,

Kripke’s Worlds

Kripke’s Worlds
  • Author : Olivier Gasquet,Andreas Herzig,Bilal Said,François Schwarzentruber
  • Publisher : Springer Science & Business Media
  • Release : 20 November 2013
GET THIS BOOKKripke’s Worlds

Possible worlds models were introduced by Saul Kripke in the early 1960s. Basically, a possible world's model is nothing but a graph with labelled nodes and labelled edges. Such graphs provide semantics for various modal logics (alethic, temporal, epistemic and doxastic, dynamic, deontic, description logics) and also turned out useful for other nonclassical logics (intuitionistic, conditional, several paraconsistent and relevant logics). All these logics have been studied intensively in philosophical and mathematical logic and in computer science, and have been

Logical Foundations of Computer Science

Logical Foundations of Computer Science
  • Author : Sergei Artemov,Anil Nerode
  • Publisher : Springer Nature
  • Release : 13 December 2019
GET THIS BOOKLogical Foundations of Computer Science

This book constitutes the refereed proceedings of the International Symposium on Logical Foundations of Computer Science, LFCS 2020, held in Deerfield Beach, FL, USA, in January 2020. The 17 revised full papers were carefully reviewed and selected from 30 submissions. The scope of the Symposium is broad and includes constructive mathematics and type theory; homotopy type theory; logic, automata, and automatic structures; computability and randomness; logical foundations of programming; logical aspects of computational complexity; parameterized complexity; logic programming and constraints; automated deduction and interactive

Categories for the Working Philosopher

Categories for the Working Philosopher
  • Author : Elaine Landry
  • Publisher : Oxford University Press
  • Release : 19 October 2017
GET THIS BOOKCategories for the Working Philosopher

This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these