Internal Logic

This second volume of a collection of papers offers new perspectives and challenges in the study of logic. It is presented in honor of the fiftieth birthday of Jean-Yves Béziau. The papers touch upon a wide range of topics including paraconsistent logic, quantum logic, geometry of oppositions, categorical logic, computational logic, fundamental logic notions (identity, rule, quantification) and history of logic (Leibniz, Peirce, Hilbert). The volume gathers personal recollections about Jean-Yves Béziau and an autobiography, followed by 25 papers written by internationally distinguished logicians, mathematicians, computer scientists, linguists and philosophers, including Irving Anellis, Dov Gabbay, Ivor Grattan-Guinness, Istvan Németi, Henri Prade. These essays will be of interest to all students and researchers interested in the nature and future of logic.

Mathematical Logic and Theoretical Computer Science covers various topics ranging from recursion theory to Zariski topoi. Leading international authorities discuss selected topics in a number of areas, including denotational semanitcs, reccuriosn theoretic aspects fo computer science, model theory and algebra, Automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. The most up-to-date review available in its field, Mathematical Logic and Theoretical Computer Science will be of interest to mathematical logicians, computer scientists, algebraists, algebraic geometers, differential geometers, differential topologists, and graduate students in mathematics and computer science.

This book constitutes the strictly refereed post-workshop proceedings of the 12th International Workshop on Computer Science Logic, CSL '98, held as the Annual Conference of the European Association on Computer Science Logic in Brno, Czech Republic in August 1998. The 25 revised full papers presented were carefully reviewed and selected during two rounds of reviewing and revision. Also included are three reviewed invited papers. The papers span the whole scope of computer science logic and mathematical foundations and represent the state of the art in the area.

What follows from what, and how do we make statements (whether true or false) about which inferences are correct? In this book, Edwin Mares provides a new philosophical, semantical and historical analysis of and justification for the relevant logic of entailment. In the first half of the book he examines some key ideas in the historical development of the logic of entailment, looking in particular at the notion 'is derivable from' and at how symbolic logic has attempted to capture this notion. In the second half of the book he develops his own theory connecting ideas from the traditions in mathematical logic with some ideas in the philosophy of science. The book's fresh and original perspective on the logic of entailment will be valuable for all who want to know more about the historical and philosophical origins of modern symbolic logic.

Mathematical Principles of Fuzzy Logic provides a systematic study of the formal theory of fuzzy logic. The book is based on logical formalism demonstrating that fuzzy logic is a well-developed logical theory. It includes the theory of functional systems in fuzzy logic, providing an explanation of what can be represented, and how, by formulas of fuzzy logic calculi. It also presents a more general interpretation of fuzzy logic within the environment of other proper categories of fuzzy sets stemming either from the topos theory, or even generalizing the latter. This book presents fuzzy logic as the mathematical theory of vagueness as well as the theory of commonsense human reasoning, based on the use of natural language, the distinguishing feature of which is the vagueness of its semantics.

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

The first edition of the Handbook of Philosophical Logic (four volumes) was published in the period 1983-1989 and has proven to be an invaluable reference work to both students and researchers in formal philosophy, language and logic. The second edition of the Handbook is intended to comprise some 18 volumes and will provide a very up-to-date authoritative, in-depth coverage of all major topics in philosophical logic and its applications in many cutting-edge fields relating to computer science, language, argumentation, etc. The volumes will no longer be as topic-oriented as with the first edition because of the way the subject has evolved over the last 15 years or so. However the volumes will follow some natural groupings of chapters. Audience: Students and researchers whose work or interests involve philosophical logic and its applications

This book contains the papers presented at the 14th International Conference on Field Programmable Logic and Applications (FPL) held during August 30th- September 1st 2004. The conference was hosted by the Interuniversity Micro- Electronics Center (IMEC) in Leuven, Belgium. The FPL series of conferences was founded in 1991 at Oxford University (UK), and has been held annually since: in Oxford (3 times), Vienna, Prague, Darmstadt, London, Tallinn, Glasgow, Villach, Belfast, Montpellier and Lisbon. It is the largest and oldest conference in reconfigurable computing and brings together academic researchers, industry experts, users and newcomers in an informal, welcoming atmosphere that encourages productive exchange of ideas and knowledge between the delegates. The fast and exciting advances in field programmable logic are increasing steadily with more and more application potential and need. New ground has been broken in architectures, design techniques, (partial) run-time reconfiguration and applications of field programmable devices in several different areas. Many of these recent innovations are reported in this volume. The size of the FPL conferences has grown significantly over the years. FPL in 2003 saw 216 papers submitted. The interest and support for FPL in the programmable logic community continued this year with 285 scientific papers submitted, demonstrating a 32% increase when compared to the year before. The technical program was assembled from 78 selected regular papers, 45 additional short papers and 29 posters, resulting in this volume of proceedings. The program also included three invited plenary keynote presentations from Xilinx, Gilder Technology Report and Altera, and three embedded tutorials from Xilinx, the Universit ̈ at Karlsruhe (TH) and the University of Oslo.