Download or read book Modal Logics as Labelled Deductive Systems written by and published by . This book was released on 1996 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Labelled Non Classical Logics written by Luca Viganò and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 isolated uses of labels by various distinguished authors, as a means to achieve local proof theoretic goals. Labelling was used in many different areas such as resource labelling in relevance logics, prefix tableaux in modal logics, annotated logic programs in logic programming, proof tracing in truth maintenance systems, and various side annotations in higher-order proof theory, arithmetic and analysis. This widespread local use of labels was an indication of an underlying logical pattern, namely the simultaneous side-by-side manipulation of several kinds of logical information. It was clear that there was a need to establish the labelled deductive systems methodology. Modal logic is one major area where labelling can be developed quickly and sys tematically with a view of demonstrating its power and significant advantage. In modal logic the labels can play a double role.
Download or read book Labelled Propositional Modal Logics written by David Basin and published by . This book was released on 1996 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "We show how labelled deductive systems can be combined with a logical framework to provide a natural deduction implementation of a large and well-known class of propositional modal logics (including K, D, T, B, S4, S4.2, K D45, S5). Our approach is modular and based on a separation between a base logic and a labelling algebra, which interact through a fixed interface. While the base logic stays fixed, different modal logics are generated by plugging in appropriate algebras. This leads to a hierarchical structuring of modal logics with inheritance of theorems. Moreover, it allows modular correctness proofs, both with respect to soundness and completeness for semantics, and faithfulness and adequacy of the implementation. We also investigate the tradeoffs in possible labelled presentations: We show that a narrow interface between the base logic and the labelling algebra supports modularity and provides an attractive proof-theory (in comparison to, e.g., semantic embedding) but limits the degree to which we can make use of extensions to the labelling algebra."
Download or read book Compiled Labelled Deductive Systems written by Krysia Broda and published by Institute of Physics Publishing (GB). This book was released on 2004 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a general framework, called Compiled Labelled Deductive System (CLDS), for a unified presentation of logics. It shows how this technique is applied to various families of non-classical logics widely used in Computer Science and Artificial Intelligence. It includes complete natural deduction proof systems, together with proofs and examples, for the families of propositional and predicate modal logics, propositional conditional logics of normality, multiplicative linear logic and for Lukasiewicz fuzzy logic. The CLDS framework generalises the notion of a logical theory to a structured theory consisting of labelled formulas and relations between the labels. This formalisation makes the logics more amenable to applications. Moreover, the framework provides a semantic approach based on a first-order translation, which can be uniformly applied to any logic whose semantics is first-order axiomatisable. Such a semantic approach also facilitates the development of automated theorem provers for non-classical logics.
Download or read book Labelled Deduction written by David Basin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: Labelled deduction is an approach to providing frameworks for presenting and using different logics in a uniform and natural way by enriching the language of a logic with additional information of a semantic proof-theoretical nature. Labelled deduction systems often possess attractive properties, such as modularity in the way that families of related logics are presented, parameterised proofs of metatheoretic properties, and ease of mechanisability. It is thus not surprising that labelled deduction has been applied to problems in computer science, AI, mathematical logic, cognitive science, philosophy and computational linguistics - for example, formalizing and reasoning about dynamic `state oriented' properties such as knowledge, belief, time, space, and resources.
Download or read book Natural Deduction Hybrid Systems and Modal Logics written by Andrzej Indrzejczak and published by Springer Science & Business Media. This book was released on 2010-07-03 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed exposition of one of the most practical and popular methods of proving theorems in logic, called Natural Deduction. It is presented both historically and systematically. Also some combinations with other known proof methods are explored. The initial part of the book deals with Classical Logic, whereas the rest is concerned with systems for several forms of Modal Logics, one of the most important branches of modern logic, which has wide applicability.
Download or read book Labelled Deductive Systems written by Dov M. Gabbay and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work introduces a new unifying framework for logics which makes it particularly suitable for applications. It develops its general theory and illustrates it with applications in logic, computer science, artificial intelligence, and philosophy.
Download or read book Displaying Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support.
Download or read book Deductive Systems in Traditional and Modern Logic written by Alex Citkin and published by MDPI. This book was released on 2020-11-18 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic.
Download or read book Many Dimensional Modal Logics Theory and Applications written by A. Kurucz and published by Elsevier. This book was released on 2003-10-21 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables
Download or read book Modal Logic written by Nino B. Cocchiarella and published by Oxford University Press. This book was released on 2008-08-04 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, a variety of modal logics at the sentential, first-order, and second-order levels are developed with clarity, precision and philosophical insight. All of the S1-S5 modal logics of Lewis and Langford, among others, are constructed. A matrix, or many-valued semantics, for sentential modal logic is formalized, and an important result that no finite matrix can characterize any of the standard modal logics is proven. Exercises, some of which show independence results, help to develop logical skills. A separate sentential modal logic of logical necessity in logical atomism is also constructed and shown to be complete and decidable. On the first-order level of the logic of logical necessity, the modal thesis of anti-essentialism is valid and every de re sentence is provably equivalent to a de dicto sentence. An elegant extension of the standard sentential modal logics into several first-order modal logics is developed. Both a first-order modal logic for possibilism containing actualism as a proper part as well as a separate modal logic for actualism alone are constructed for a variety of modal systems. Exercises on this level show the connections between modal laws and quantifier logic regarding generalization into, or out of, modal contexts and the conditions required for the necessity of identity and non-identity. Two types of second-order modal logics, one possibilist and the other actualist, are developed based on a distinction between existence-entailing concepts and concepts in general. The result is a deeper second-order analysis of possibilism and actualism as ontological frameworks. Exercises regarding second-order predicate quantifiers clarify the distinction between existence-entailing concepts and concepts in general. Modal Logic is ideally suited as a core text for graduate and undergraduate courses in modal logic, and as supplementary reading in courses on mathematical logic, formal ontology, and artificial intelligence.
Download or read book A Proof Search System for a Modal Substructural Logic Based on Labelled Deductive Systems written by Hiu Fai Chau and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Deductive Systems and the Decidability Problem for Hybrid Logics written by Michał Zawidzki and published by . This book was released on 2013 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Proof Theory of Modal Logic written by Heinrich Wansing and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Download or read book First Steps in Modal Logic written by Sally Popkorn and published by Cambridge University Press. This book was released on 1994-12-08 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a first course in propositional modal logic, suitable for mathematicians, computer scientists and philosophers. Emphasis is placed on semantic aspects, in the form of labelled transition structures, rather than on proof theory.
Download or read book Modal Logics and Philosophy written by Rod Girle and published by Routledge. This book was released on 2014-12-05 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition, published by Acumen in 2000, became a prescribed textbook on modal logic courses. The second edition has been fully revised in response to readers' suggestions, including two new chapters on conditional logic, which was not covered in the first edition. "Modal Logics and Philosophy" is a fully comprehensive introduction to modal logics and their application suitable for course use. Unlike most modal logic textbooks, which are both forbidding mathematically and short on philosophical discussion, "Modal Logics and Philosophy" places its emphasis firmly on showing how useful modal logic can be as a tool for formal philosophical analysis. In part 1 of the book, the reader is introduced to some standard systems of modal logic and encouraged through a series of exercises to become proficient in manipulating these logics. The emphasis is on possible world semantics for modal logics and the semantic emphasis is carried into the formal method, Jeffrey-style truth-trees. Standard truth-trees are extended in a simple and transparent way to take possible worlds into account. Part 2 systematically explores the applications of modal logic to philosophical issues such as truth, time, processes, knowledge and belief, obligation and permission.
Download or read book The Functional Interpretation of Logical Deduction written by Ruy J. G. B. de Queiroz and published by World Scientific. This book was released on 2012 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive book provides an adequate framework to establish various calculi of logical inference. Being an ?enriched? system of natural deduction, it helps to formulate logical calculi in an operational manner. By uncovering a certain harmony between a functional calculus on the labels and a logical calculus on the formulas, it allows mathematical foundations for systems of logic presentation designed to handle meta-level features at the object-level via a labelling mechanism, such as the D Gabbay's Labelled Deductive Systems. The book truly demonstrates that introducing ?labels? is useful to understand the proof-calculus itself, and also to clarify its connections with model-theoretic interpretations.
