Semantical Investigations In Heytings Intuitionistic Logic
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| Author | : Dov M. Gabbay |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2013-11-11 |
| Genre | : Philosophy |
| ISBN | : 9401729778 |
From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics.
| Author | : Dov M. Gabbay |
| Publisher | : Taylor & Francis |
| Total Pages | : 312 |
| Release | : 1981 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9789027712028 |
From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be of interest to the intuitionist mathematician. Originally, I intended to include more material in that spirit but I decided against it. There is no coherent body of material to include that builds naturally on the present book. There are some serious results on topological models, second order Beth and Kripke models, theories of types, etc., but it would require further research to be able to present a general theory, possibly using sheaves. That would have postponed pUblication for too long. I would like to dedicate this book to my colleagues, Professors G. Kreisel, M.O. Rabin and D. Scott. I have benefited greatly from Professor Kreisel's criticism and suggestions. Professor Rabin's fun damental results on decidability and undecidability provided the powerful tools used in obtaining the majority of the results reported in this book. Professor Scott's approach to non-classical logics and especially his analysis of the Scott consequence relation makes it possible to present Heyting's logic as a beautiful, integral part of non-classical logics.
| Author | : Arend Heyting |
| Publisher | : |
| Total Pages | : 145 |
| Release | : 1971 |
| Genre | : |
| ISBN | : |
| Author | : Dov M. Gabbay |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 370 |
| Release | : 2013-03-14 |
| Genre | : Philosophy |
| ISBN | : 9401704589 |
It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good,! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise. The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.
| Author | : Jonathan Lear |
| Publisher | : Routledge |
| Total Pages | : 287 |
| Release | : 2010-02-13 |
| Genre | : Mathematics |
| ISBN | : 1135165858 |
Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. This title brings together articles that honour Smiley's work. It is suitable for those working across the logical spectrum - in philosophy of language, philosophical and mathematical logic, and philosophy of mathematics.
| Author | : Dov M. Gabbay |
| Publisher | : Oxford University Press |
| Total Pages | : 524 |
| Release | : 2005-05-12 |
| Genre | : Computers |
| ISBN | : 0198511744 |
This book is a specialized monograph on interpolation and definability, a notion central in pure logic and with significant meaning and applicability in all areas where logic is applied, especially computer science, artificial intelligence, logic programming, philosophy of science and natural language.Suitable for researchers and graduate students in mathematics, computer science and philosophy, this is the latest in the prestigous world-renowned Oxford Logic Guides, which contains Michael Dummet's Elements of intuitionism (second edition), J. M. Dunn and G. Hardegree's Algebraic Methods in Philosophical Logic, H. Rott's Change, Choice and Inference: A Study of Belief Revision and NonmonotonicReasoning, P. T. Johnstone's Sketches of an Elephant: A Topos Theory Compendium: Volumes 1 and 2, and David J. Pym and Eike Ritter's Reductive Logic and Proof Search: Proof theory, semantics and control.
| Author | : Dale Jacquette |
| Publisher | : John Wiley & Sons |
| Total Pages | : 832 |
| Release | : 2008-04-15 |
| Genre | : Philosophy |
| ISBN | : 1405149949 |
This collection of newly comissioned essays by international contributors offers a representative overview of the most important developments in contemporary philosophical logic. Presents controversies in philosophical implications and applications of formal symbolic logic. Surveys major trends and offers original insights.
| Author | : Antonin Kucera |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 208 |
| Release | : 2010-08-18 |
| Genre | : Computers |
| ISBN | : 3642153488 |
This volume contains the papers presented at the 4th International Workshop on Reachability Problems, RP 2010 held during August 28–29, 2010 in the F- ulty of Informatics, Masaryk University, Brno, Czech Republic and co-located with Joint MFCS and CSL 2010 (35th InternationalSymposiums on Mathem- ical Foundations of Computer Science and 19th EACSL Annual Conferences on Computer Science Logic). RP 2010 was the fourth in the series of workshops following three successful meetings at Ecole Polytechnique, France in 2009 at University of Liverpool, UK in 2008 and at Turku University, Finland in 2007. TheReachabilityProblemsworkshopsseriesaimsatgatheringtogethersch- ars from diverse disciplines and backgrounds interested in reachability problems that appearin algebraicstructures,computationalmodels, hybridsystems, logic and veri?cation, etc. Reachability is a fundamental problem in the context of many models and abstractions which describe various computational processes. Analysisofthecomputationaltracesandpredictabilityquestionsforsuchmodels can be formalized as a set of di?erent reachability problems. In general, reac- bility can be formulated as follows: Given a computational system with a set of allowed transformations (functions), decide whether a certain state of a system is reachable from a given initial state by a set of allowed transformations. The same questions can be asked not only about reachability of exact states of the system but also about a set of states expressed in terms of some property as a parameterized reachability problem. Another set of predictability questions can be seen in terms of reachability of eligible traces of computations,unavoidability ofsomedynamicsandapossibilitytoavoidundesirabledynamicsusingalimited control.
| Author | : Agata Ciabattoni |
| Publisher | : Springer Nature |
| Total Pages | : 441 |
| Release | : 2022-09-08 |
| Genre | : Philosophy |
| ISBN | : 3031152980 |
Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 28th Workshop on Logic, Language, Information and Computation, WoLLIC 2022, Iasi, Romania, in September 2022. The 25 full papers presented included with 8 extra abstracts, 5 invited talks and 3 tutorials were fully reviewed and selected from 46 submissions. The conference aims fostering interdisciplinary research in pure and applied logic.
| Author | : Alexander Kulikov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 480 |
| Release | : 2011-06-03 |
| Genre | : Computers |
| ISBN | : 3642207111 |
This book constitutes the proceedings of the 6th International Computer Science Symposium in Russia, CSR 2011, held in St. Petersburg, Russia, in June 2011. The 29 papers presented were carefully reviewed and selected from 76 submissions. The scope of topics of the symposium was quite broad and covered basically all areas of the foundations of theoretical computer science.
