Conditionals and Modularity in General Logics PDF Download

Author: Dov M. Gabbay
Publisher: Springer Science & Business Media
ISBN: 3642190685
Category : Mathematics
Languages : en
Pages : 238

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Book Description
This text centers around three main subjects. The first is the concept of modularity and independence in classical logic and nonmonotonic and other nonclassical logic, and the consequences on syntactic and semantical interpolation and language change. In particular, we will show the connection between interpolation for nonmonotonic logic and manipulation of an abstract notion of size. Modularity is essentially the ability to put partial results achieved independently together for a global result. The second aspect of the book is the authors' uniform picture of conditionals, including many-valued logics and structures on the language elements themselves and on the truth value set. The third topic explained by the authors is neighbourhood semantics, their connection to independence, and their common points and differences for various logics, e.g., for defaults and deontic logic, for the limit version of preferential logics, and for general approximation. The book will be of value to researchers and graduate students in logic and theoretical computer science.

Author: Dov M. Gabbay
Publisher: Springer
ISBN: 3319468170
Category : Mathematics
Languages : en
Pages : 367

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Book Description
In this book the authors present new results on interpolation for nonmonotonic logics, abstract (function) independence, the Talmudic Kal Vachomer rule, and an equational solution of contrary-to-duty obligations. The chapter on formal construction is the conceptual core of the book, where the authors combine the ideas of several types of nonmonotonic logics and their analysis of 'natural' concepts into a formal logic, a special preferential construction that combines formal clarity with the intuitive advantages of Reiter defaults, defeasible inheritance, theory revision, and epistemic considerations. It is suitable for researchers in the area of computer science and mathematical logic.

Author: Karl Schlechta
Publisher: Springer
ISBN: 3319896504
Category : Mathematics
Languages : en
Pages : 511

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Book Description
The two volumes in this advanced textbook present results, proof methods, and translations of motivational and philosophical considerations to formal constructions. In the associated Vol. I the author explains preferential structures and abstract size. In this Vol. II he presents chapters on theory revision and sums, defeasible inheritance theory, interpolation, neighbourhood semantics and deontic logic, abstract independence, and various aspects of nonmonotonic and other logics. In both volumes the text contains many exercises and some solutions, and the author limits the discussion of motivation and general context throughout, offering this only when it aids understanding of the formal material, in particular to illustrate the path from intuition to formalisation. Together these books are a suitable compendium for graduate students and researchers in the area of computer science and mathematical logic.

Author: Sven Ove Hansson
Publisher: Springer Science & Business Media
ISBN: 9400777590
Category : Philosophy
Languages : en
Pages : 432

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Book Description
The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the (limited but important) role of logic in philosophy.

Author: J. Michael Dunn
Publisher: OUP Oxford
ISBN: 0191589225
Category :
Languages : en
Pages : 490

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Book Description
This comprehensive text demonstrates how various notions of logic can be viewed as notions of universal algebra. It is aimed primarily for logisticians in mathematics, philosophy, computer science and linguistics with an interest in algebraic logic, but is also accessible to those from a non-logistics background. It is suitable for researchers, graduates and advanced undergraduates who have an introductory knowledge of algebraic logic providing more advanced concepts, as well as more theoretical aspects. The main theme is that standard algebraic results (representations) translate into standard logical results (completeness). Other themes involve identification of a class of algebras appropriate for classical and non-classical logic studies, including: gaggles, distributoids, partial- gaggles, and tonoids. An imporatant sub title is that logic is fundamentally information based, with its main elements being propositions, that can be understood as sets of information states. Logics are considered in various senses e.g. systems of theorems, consequence relations and, symmetric consequence relations.

Author: H. Prakken
Publisher: Springer Science & Business Media
ISBN: 9401589755
Category : Philosophy
Languages : en
Pages : 319

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Book Description
This book is a revised and extended version of my PhD Thesis 'Logical Tools for Modelling Legal Argument', which I defended on 14 January 1993 at the Free University Amsterdam. The first five chapters of the thesis have remained almost completely unchanged but the other chapters have undergone considerable revision and expansion. Most importantly, I have replaced the formal argument-based system of the old Chapters 6, 7 and 8 with a revised and extended system, whieh I have developed during the last three years in collaboration with Giovanni Sartor. Apart from some technical improvements, the main additions to the old system are the enriehment of its language with a nonprovability operator, and the ability to formalise reasoning about preference criteria. Moreover, the new system has a very intuitive dialectieal form, as opposed to the rather unintuitive fixed-point appearance of the old system. Another important revision is the split of the old Chapter 9 into two new chapters. The old Section 9. 1 on related research has been updated and expanded into a whole chapter, while the rest of the old chapter is now in revised form in Chapter 10. This chapter also contains two new contributions, a detailed discussion of Gordon's Pleadings Game, and a general description of a multi-Iayered overall view on the structure of argu mentation, comprising a logieal, dialectical, procedural and strategie layer. Finally, in the revised conclusion I have paid more attention to the relevance of my investigations for legal philosophy and argumentation theory.

Author: Xiangdong He
Publisher: Springer Science & Business Media
ISBN: 3642048927
Category : Mathematics
Languages : en
Pages : 339

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Book Description
Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the Second International Workshop on Logic, Rationality, and Interaction, LORI 2009, held in Chongqing, China, in October 2009. The 24 revised full papers presented together with 8 posters were carefully reviewed and selected from a flood of submissions. The workshops topics include but are not limited to semantic models for knowledge, for belief, and for uncertainty, dynamic logics of knowledge, information flow, and action, logical analysis of the structure of games, belief revision, belief merging, logics for preferences and utilities, logics of intentions, plans, and goals, logics of probability and uncertainty, argument systems and their role in interaction, as well as norms, normative interaction, and normative multiagent systems.

Author: Kurt Engesser
Publisher: Elsevier
ISBN: 008055038X
Category : Mathematics
Languages : en
Pages : 821

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Book Description
Since its inception in the famous 1936 paper by Birkhoff and von Neumann entitled "The logic of quantum mechanics quantum logic, i.e. the logical investigation of quantum mechanics, has undergone an enormous development. Various schools of thought and approaches have emerged and there are a variety of technical results.Quantum logic is a heterogeneous field of research ranging from investigations which may be termed logical in the traditional sense to studies focusing on structures which are on the border between algebra and logic. For the latter structures the term quantum structures is appropriate. The chapters of this Handbook, which are authored by the most eminent scholars in the field, constitute a comprehensive presentation of the main schools, approaches and results in the field of quantum logic and quantum structures. Much of the material presented is of recent origin representing the frontier of the subject. The present volume focuses on quantum structures. Among the structures studied extensively in this volume are, just to name a few, Hilbert lattices, D-posets, effect algebras MV algebras, partially ordered Abelian groups and those structures underlying quantum probability.- Written by eminent scholars in the field of logic- A comprehensive presentation of the theory, approaches and results in the field of quantum logic- Volume focuses on quantum structures

Author: Jean-Pierre Jouannaud
Publisher: Springer Science & Business Media
ISBN: 9783540584032
Category : Computers
Languages : en
Pages : 394

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Book Description
This volume constitutes the proceedings of the First International Conference on Constraints in Computational Logics, CCL '94, held in Munich, Germany in September 1994. Besides abstracts or full papers of the 5 invited talks by senior researchers, the book contains revised versions of the 21 accepted research papers selected from a total of 52 submissions. The volume assembles high quality original papers covering major theoretical and practical issues of combining and extending programming paradigms, preferably by using constraints. The topics covered include symbolic constraints, set constraints, numerical constraints, multi-paradigm programming, combined calculi, constraints in rewriting, deduction, symbolic computations, and working systems.

Author: Andrei Voronkov
Publisher: Springer Science & Business Media
ISBN: 9783540557272
Category : Computers
Languages : en
Pages : 532

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Book Description
This volume contains the proceedings of LPAR '92, the international conference on logic programming and automated reasoning held in St. Petersburg in July 1992. The aim of the conference was to bring together researchers from the Russian and the international logic programming and theorem proving communities. The topics of interest covered by papers inthe volume include automated theorem proving, non-monotonic reasoning, applications of mathematical logic to computer science, deductive databases, implementation of declarative concepts, and programming in non-classical logics. LPAR '92 is the successor of the First and Second Russian Conferences on Logic Programming held in 1990 and 1991, respectively, the proceedings of which were publishedin LNAI Vol. 592.