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Labelled Deductive Systems
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Book Synopsis Compiled Labelled Deductive Systems by : Krysia Broda
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.
Book Synopsis Labelled Deductive Systems by : Dov M. Gabbay
Download or read book Labelled Deductive Systems written by Dov M. Gabbay and published by . This book was released on 1996 with total page 520 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.
Book Synopsis Labelled Non-Classical Logics by : Luca Viganò
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.
Book Synopsis Labelled Deductive Systems by : Dov M. Gabbay
Download or read book Labelled Deductive Systems written by Dov M. Gabbay and published by . This book was released on 1991 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Labelled Non-Classical Logics by : Luca Viganò
Download or read book Labelled Non-Classical Logics written by Luca Viganò and published by Springer Science & Business Media. This book was released on 2000-01-31 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to establish advantages and limitations of our approach with respect to related ones, but also to give, by means of a substructural analysis, a new proof-theoretic method for investigating decidability and complexity of (some of) the logics we consider. All of our deduction systems have been implemented in the generic theorem prover Isabelle, thus providing a simple and natural environment for interactive proof development. Labelled Non-Classical Logics is essential reading for researchers and practitioners interested in the theory and applications of non-classical logics.
Book Synopsis The Functional Interpretation of Logical Deduction by : Ruy J. G. B. de Queiroz
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.
Book Synopsis Natural Deduction, Hybrid Systems and Modal Logics by : Andrzej Indrzejczak
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.
Book Synopsis Situation Theory and Its Applications: Volume 3 by : Robin Cooper
Download or read book Situation Theory and Its Applications: Volume 3 written by Robin Cooper and published by Center for the Study of Language (CSLI). This book was released on 1990 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Situation theory is the result of an interdisciplinary effort to create a full-fledged theory of information. Created by scholars and scientists from cognitive science, computer science and AI, linguistics, logic, philosophy, and mathematics, it aims to provide a common set of tools for the analysis of phenomena from all these fields. Unlike Shannon-Weaver type theories of information, which are purely quantitative theories, situation theory aims at providing tools for the analysis of the specific content of a situation (signal, message, data base, statement, or other information-carrying situation). The question addressed is not how much information is carried, but what information is carried.
Book Synopsis Computational Logic by : Dov M. Gabbay
Download or read book Computational Logic written by Dov M. Gabbay and published by Newnes. This book was released on 2014-12-09 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of the History of Logic brings to the development of logic the best in modern techniques of historical and interpretative scholarship. Computational logic was born in the twentieth century and evolved in close symbiosis with the advent of the first electronic computers and the growing importance of computer science, informatics and artificial intelligence. With more than ten thousand people working in research and development of logic and logic-related methods, with several dozen international conferences and several times as many workshops addressing the growing richness and diversity of the field, and with the foundational role and importance these methods now assume in mathematics, computer science, artificial intelligence, cognitive science, linguistics, law and many engineering fields where logic-related techniques are used inter alia to state and settle correctness issues, the field has diversified in ways that even the pure logicians working in the early decades of the twentieth century could have hardly anticipated. Logical calculi, which capture an important aspect of human thought, are now amenable to investigation with mathematical rigour and computational support and fertilized the early dreams of mechanised reasoning: "Calculemus. The Dartmouth Conference in 1956 – generally considered as the birthplace of artificial intelligence – raised explicitly the hopes for the new possibilities that the advent of electronic computing machinery offered: logical statements could now be executed on a machine with all the far-reaching consequences that ultimately led to logic programming, deduction systems for mathematics and engineering, logical design and verification of computer software and hardware, deductive databases and software synthesis as well as logical techniques for analysis in the field of mechanical engineering. This volume covers some of the main subareas of computational logic and its applications. - Chapters by leading authorities in the field - Provides a forum where philosophers and scientists interact - Comprehensive reference source on the history of logic
Book Synopsis Logic, Language and Reasoning by : Hans Jürgen Ohlbach
Download or read book Logic, Language and Reasoning written by Hans Jürgen Ohlbach and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: th This volume is dedicated to Dov Gabbay who celebrated his 50 birthday in October 1995. Dov is one of the most outstanding and most productive researchers we have ever met. He has exerted a profound influence in major fields of logic, linguistics and computer science. His contributions in the areas of logic, language and reasoning are so numerous that a comprehensive survey would already fill half of this book. Instead of summarizing his work we decided to let him speak for himself. Sitting in a car on the way to Amsterdam airport he gave an interview to Jelle Gerbrandy and Anne-Marie Mineur. This recorded conversation with him, which is included gives a deep insight into his motivations and into his view of the world, the Almighty and, of course, the role of logic. In addition, this volume contains a partially annotated bibliography of his main papers and books. The length of the bibliography and the broadness of the topics covered there speaks for itself.
Book Synopsis Logic Colloquium 2005 by : Costas Dimitracopoulos
Download or read book Logic Colloquium 2005 written by Costas Dimitracopoulos and published by Cambridge University Press. This book was released on 2008 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.
Book Synopsis Proof and System-Reliability by : Helmut Schwichtenberg
Download or read book Proof and System-Reliability written by Helmut Schwichtenberg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: As society comes to rely increasingly on software for its welfare and prosperity there is an urgent need to create systems in which it can trust. Experience has shown that confidence can only come from a more profound understanding of the issues, which in turn can come only if it is based on logically sound foundations. This volume contains contributions from leading researchers in the critical disciplines of computing and information science, mathematics, logic, and complexity. All contributions are self-contained, aiming at comprehensibility as well as comprehensiveness. The volume also contains introductory hints to technical issues, concise surveys, introductions, and various fresh results and new perspectives.
Book Synopsis Philosophical and Formal Approaches to Linguistic Analysis by : Piotr Stalmaszczyk
Download or read book Philosophical and Formal Approaches to Linguistic Analysis written by Piotr Stalmaszczyk and published by Walter de Gruyter. This book was released on 2013-05-02 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles gathered in the volume focus on traditional and contemporary debates within the philosophy of language, and on the interfaces between linguistics, philosophy, and logic. The topics of individual contributions cover such diverse issues as analytic accounts of the a priori and implicit definitions, medieval and contemporary theories of fallacy, game-theoretical semantics, modal games in natural language and literary semantics, possible-world theories and paradoxes involving structured propositions, extensions to Dynamic Syntax, semantics of proper names, judgement-dependence, tacit knowledge and linguistic understanding, ontology in semantics, implicit knowledge and theory of meaning, and many more. The multitude of topics shows that the convergence of linguistic, philosophical, formal, and cognitive approaches opens new research perspectives within contemporary philosophy of language and linguistics. The volume includes contributions by (among other authors): Luis Fernández Moreno (Madrid), Chris Fox (Essex), Ruth Kempson (London), Alexander Miller (Birmingham), Arthur Sullivan (Newfoundland), Mieszko Talasiewicz (Warsaw).
Book Synopsis Current Issues in Mathematical Linguistics by : C. Martín-Vide
Download or read book Current Issues in Mathematical Linguistics written by C. Martín-Vide and published by Elsevier. This book was released on 2014-06-28 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume contains some selected topics of current interest around the world in the mathematical analysis of natural language. The book is divided into four sections:- analytical algebraic models- models from the theory of formal grammars and automata, with interest mainly in syntax- model-theoretic concepts in semantics or pragmatics, and- a final section containing some applications in computational linguistics.The varied perspectives illustrated in the book confirm that Mathematical Linguistics has finally introduced scientific methods into a previously fuzzy field, through the use of mathematical reasoning. The text will contribute to a fruitful convergence between linguists, mathematicians, logicians, computer scientists, cognitive scientists and others interested in the formal treatment of natural language and the research of its properties.
Book Synopsis Logical Aspects of Computational Linguistics by : Christian Retore
Download or read book Logical Aspects of Computational Linguistics written by Christian Retore and published by Springer Science & Business Media. This book was released on 1997-10-15 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the strictly refereed post-conference proceedings of the First International Conference on Logical Aspects of Computational Linguistics, LACL '96, held in Nancy, France in April 1996. The volume presents 18 revised full papers carefully selected and reviewed for inclusion in the book together with four invited contributions by leading authorities and an introductory survey with a detailed bibliography. The papers cover all relevant logical aspects of computational linguistics like logical inference, grammars, logical semantics, natural language processing, formal proofs, logic programming, type theory, etc.
Book Synopsis Agenda Relevance: A Study in Formal Pragmatics by :
Download or read book Agenda Relevance: A Study in Formal Pragmatics written by and published by Elsevier. This book was released on 2003-05-29 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: Agenda Relevance is the first volume in the authors' omnibus investigation ofthe logic of practical reasoning, under the collective title, A Practical Logicof Cognitive Systems. In this highly original approach, practical reasoning isidentified as reasoning performed with comparatively few cognitive assets,including resources such as information, time and computational capacity. Unlikewhat is proposed in optimization models of human cognition, a practical reasonerlacks perfect information, boundless time and unconstrained access tocomputational complexity. The practical reasoner is therefore obliged to be acognitive economizer and to achieve his cognitive ends with considerableefficiency. Accordingly, the practical reasoner avails himself of variousscarce-resource compensation strategies. He also possesses neurocognitivetraits that abet him in his reasoning tasks. Prominent among these is thepractical agent's striking (though not perfect) adeptness at evading irrelevantinformation and staying on task. On the approach taken here, irrelevancies areimpediments to the attainment of cognitive ends. Thus, in its most basic sense,relevant information is cognitively helpful information. Information can then besaid to be relevant for a practical reasoner to the extent that it advances orcloses some cognitive agenda of his. The book explores this idea with aconceptual detail and nuance not seen the standard semantic, probabilistic andpragmatic approaches to relevance; but wherever possible, the authors seek tointegrate alternative conceptions rather than reject them outright. A furtherattraction of the agenda-relevance approach is the extent to which its principalconceptual findings lend themselves to technically sophisticated re-expressionin formal models that marshal the resources of time and action logics andlabel led deductive systems. Agenda Relevance is necessary reading for researchers in logic, beliefdynamics, computer science, AI, psychology and neuroscience, linguistics,argumentation theory, and legal reasoning and forensic science, and will repaystudy by graduate students and senior undergraduates in these same fields.Key features:• relevance • action and agendas • practical reasoning • belief dynamics • non-classical logics • labelled deductive systems
