Investigations In Modal And Tense Logics With Applications To Problems In Philosophy And Linguistics
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Investigations in Modal and Tense Logics with Applications to Problems in Philosophy and Linguistics
Author: Dov M. Gabbay
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This book is intended to serve as an advanced text and reference work on modal logic, a subject of growing importance which has applications to philosophy and linguistics. Although it is based mainly on research which I carried out during the years 1969-1973, it also includes some related results obtained by other workers in the field (see the refer ences in Part 7). Parts 0, 1 and 2, can be used as the basis of a one year graduate course in modal logic. The material which they contain has been taught in such courses at Stanford since 1970. The remaining parts of the book contain more than enough material for a second course in modal logic. The exercises supplement the text and are usually difficult. I wish to thank Stanford University and Bar-Han University for making it possible for me to continue and finish this work, and A. Ungar for correcting the typescript. Bar-Ilan University, Israel Dov M. GABBA Y PART 0 AN INTRODUCTION TO GENERAL INTENSIONAL LOGICS CHAPTER 0 CONSEQUENCE RELATIONS Motivation We introduce the notions of a consequence relation (which is a generalization of the notion of a logical system) and of a semantics. We show that every consequence relation is complete for a canonical semantics. We define the notion of one semantics being Dian in another and study the basic properties of this notion. The concepts of this chapter are generalizations of the various notions of logical system and possible world semantics found in the literature.
Semantical Investigations in Heyting's Intuitionistic Logic
Author: Dov M. Gabbay
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-11-11
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.
Justice, Law, and Argument
Author: Ch. Perelman
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
This collection contains studies on justice, juridical reasoning and argumenta tion which contributed to my ideas on the new rhetoric. My reflections on justice, from 1944 to the present day, have given rise to various studies. The ftrst of these was published in English as The Idea of Justice and the Problem of Argument (Routledge & Kegan Paul, London, 1963). The others, of which several are out of print or have never previously been published, are reunited in the present volume. As justice is, for me, the prime example of a "confused notion", of a notion which, like many philosophical concepts, cannot be reduced to clarity without being distorted, one cannot treat it without recourse to the methods of reasoning analyzed by the new rhetoric. In actuality, these methods have long been put into practice by jurists. Legal reasoning is fertile ground for the study of argumentation: it is to the new rhetoric what mathematics is to formal logic and to the theory of demonstrative proof. It is important, then, that philosophers should not limit their methodologi cal studies to mathematics and the natural sciences. They must not neglect law in the search for practical reason. I hope that these essays lead to be a better understanding of how law can enrich philosophical thought. CH. P.