Section I : Views OF LOGIC TODAY :
1. What is Mathematical Logic? A Survey/John N. Crossley
2. Is there a Logic of Society?/Rohit Parikh
Section II : LOGIC AND Mathematics :
3. What is a Proof?/John N. Crossley
4. Deductive Systems of Fuzzy Logic/Petr Hajek
5. A Visit to Tarski's Seminar on Elimination of Quantifiers/Wilfrid Hodges
Section III : PERSPECTIVES FROM INDIAN LOGIC :
6. History and Development of Indian Logic : An Overview/K. Ramasubramanian
7. The Concept of Hetvabhasa in Nyaya-sastra/K. Ramasubramanian
8. Indian Logic and Philosophy of Science : The Logic-Epistemology Link/Sundar Sarukkai
Section IV : LOGIC AND COMPUTATION :
9. What is the Difference between Proofs and Programs?/John N. Crossley
10. Zero-One Laws : Thesauri and Parametric Conditions/Andreas Blass and Yuri Gurevich
11. Two Applications of Epistemic Logic in Computer Security/Ron Van Der Meyden
12. Recent Developments of Feedback Coding and its Relations with Many-Valued Logic/Ferdinando Cicalese and Daniele Mundici
13. An Introduction to Quantum Computing/Noson S. Yanofsky
Section V : LOGIC, AGENCY AND GAMES :
14. Logic Games : From Tools to Models of Interaction/Johan Van Benthem
15. Towards a Logical Analysis of Adjusted Winner/Eric Pacuit
16. Iterated Belief Revision in Dynamic Doxastic Logic/Krister Segerberg
17. Temporal Logic with Preferences and Reasoning about Games/G. Venkutesh
Section VI : LOGIC, LANGUAGE AND Cognition :
18. Some Reflections on Discrete Mathematical Models in Behavioral, Cognitive and Social Sciences/B. D. Acharya and Shalini Joshi
19. From Sentence Meanings to Full Semantics/Wilfrid Hodges
The 'First Indian Conference on Logic and its Relationship with Other Disciplines' took place in Mumbai at IIT Bombay, from January 8 to 12, 2005, as an initiative of the Mumbai logic circle, bringing together Indian logicians from various disciplinary backgrounds and different locations with a group of open-minded and active international colleagues.
The conference took place over six days : two of them devoted to tutorials and four to advanced talks. Tutorials as well as advanced talks were given by Indian logicians and by visitors from abroad. The visitors responding to the Call for the Mumbai event came from Australia, the Czech Republic, Finland, Great Britain, Italy, Israel, Japan, the Netherlands, the USA, and other nations. Together, they formed a distinguished galaxy seldom found even with conferences in the West. The papers emphasized novel approaches and perspectives emanating from research by some of the masters of logic and its interfaces with surrounding disciplines.
The Conference took place at the outstanding logistical and scenic facilities at IIT Bombay, with smooth organizational efforts and crucial support provided by faculty, and especially also by student volunteers. The geese, the pond, and the view of the lake provided most people with the needed inspiration to think of deeper matters.
Talks ranged from reflections on the range of mathematical proof and definability to recent developments in computational logic, as well as new interfaces between logic, information dynamics, and games. In addition, there was a wide range of presentations on schools of Indian logic. One term used nowadays for this broad view of logic is 'intelligent interaction'. The Mumbai Conference took this term in the double sense of both information exchange and community formation, and indeed both processes were in evidence. Accordingly, the 'Second Indian Conference on Logic and its Relationship with Other Disciplines' was held from January 9 to 11 in 2007 at IIT Bombay, Mumbai, with equal success. Besides these two Conferences, a first Indian Winter School with the same topic and title was held at IIT Bombay, Mumbai from January 1 to 15, 2006, primarily for students and researchers.
The current volume contains a representative selection of material from the first Conference, while the planned further volumes in this new book series will document the follow-up. Again, we see this publication venture as providing information, but also as a means of shaping a community. Our aim is to present an Indian audience with what we see as a representative sample of modern logic, in the hands of some of its best practitioners. This volume is not a textbook, however, accessible throughout to absolute beginners. But we do hope and expect that the papers collected here will give a sense of vitality, strength and direction, and that, through the story-lines and references, our chapters will open further doors to the field as the reader gets inspired.
But we also hope that this volume will help the Indian logic community take shape and flight, and indeed, there are some very encouraging signs. An 'Association for Logic in India' has recently been formed. The IIT Bombay initiative as well as other congenial events that have taken place in Kolkata 2007 as also the events which are being planned would come under its aegis. Thus the Mumbai founding events will find a natural future continuation in a national series of conferences and schools.
Finally, on a still larger scale, we hope that the present publication initiative will maintain the ties between the Indian community and its friends and colleagues worldwide. In particular, we see the papers on Indian Logic in this volume as reaching out to more classical communities in the field while informing their modern colleagues. One day, we envision that logic will have one history, with Gotama and Gangesa along with Aristotle and Boole. Be that as it may be, our book may be a first gentle push toward joining forces between historically different, but maybe in the final analysis, not all that different strands in our fascinating field.
1. B.D. Acharya, joined the Department of Science & Technology, Government of India, in 1992 as a Director and became an Advisor in 1997. He is Head of the Earth System Science Division of DST. His main current interest is the application of discrete mathematics to social and behavioural sciences
2. Johan van Benthem, is a University Professor of Logic in Amsterdam, and a Professor of Philosophy at Stanford University. He has worked in modal logic, logic and natural language, and interfaces between logic and philosophy. His main current interests are dynamic logics of information and games
3. Andreas Blass, is Professor of Mathematics, University of Michigan, and Visiting Researcher at Microsoft Research. His primary interest is mathematical logic (particularly, set theory), and applications to algebra, computer science, and other areas. Other areas : finite combinatorics, topos theory
4. Ferdinando Cicalese, is Associate Professor in Computer Science and Applications of the University of Salerno. His areas of interest are combinatorial search algorithms, and their applications in bio-informatics
5. John N. Crossley, is Emeritus Professor, Clayton School of Information Technology, Monash University. His main areas of interest are Mathematical Logic and Theoretical Computer Science
6. Yuri Gurevich, is Head of the Foundations of Software Engineering group at Microsoft Research, Washington and Professor Emeritus, University of Michigan. He started his career as an algebraist, later became a logician, and then moved to computer science, where his main projects have been Abstract State Machines, Average Case Computational Complexity, and Finite Model Theory
7. Petr Hajek, is Professor at the Institute of Computer Science, Academy of Sciences, Prague, the Czech Republic. Areas of interest : Mathematics - mathematical logic; Computer Science and Artificial Intelligence, and the mathematics of Fuzzy Logic
8. Wilfrid Hodges, is Professor of Mathematics at Queen Mary, University of London and known for his work in model theory. His areas of interest are : Mathematical logic, Foundations, and Model Theory
9. Shalini Joshi, was in the Department of Studies in Mathematics, University of Mysore, before she moved to the Department of Psychology, University of Allahabad. Her current interest is in the application of discrete mathematics to social and behavioural and cognitive science.
10. Ron van der Meyden, is an Associate Professor in the School of Computer Science and Engineering, University of New South Wales, Sydney, Australia. His areas of interest are Logic in Computer Science, Logic of Knowledge and Belief, Temporal Logic, Theory of Distributed Systems, Computer Security, Electronic Commerce Infrastructure, Deductive Databases and Logic Programming
11. Daniele Mundici, is Professor of Mathematical Logic in the Department of Mathematics, University of Florence. His areas of interest are : Mathematics and Computer Science, with particular reference to many valued logic, lattice-ordered groups, coding with feedback, polyhedra and AF C*-algebras
12. Eric Pacuit, is currently a Postdoctral Researcher at Stanford University. Previously, he was a Postdoctoral Researcher at the Institute for Logic, Language and Computation at the University of Amsterdam and Brooklyn College, CUNY, and NYU. His research interests include modal logic, game theory and its foundations, (computational) social choice, and social procedures, such as fair division algorithms and voting procedures
13. Rohit Parikh, is a Distinguished Professor of Computer Science, Mathematics and Philosophy, City University Graduate Center, and Department of Computer and Information Science, Brooklyn College, New York. Areas of current interest : Social Software, Reasoning about Knowledge, Belief Revision, Game Theory and Philosophy of Language. His earlier research was in Recursive Function Theory, Proof Theory, Formal Languages, Non-Standard Analysis, and Dynamic Logic
14. K. Ramasubramanian, is an Assistant Professor, Cell for Indian Science and Technology in the Department of Humanities and Social Sciences at Indian Institute of Technology Bombay. His areas of current interest are : Nonlinear Dynamics, and Indian Astronomy and Mathematics. He is also interested in Indian Sciences and Physics. He is a scholar in Advaita-vedanta-sastra
15. Sundar Sarukkai, is a Professor, School of Humanities, Centre for Philosophy, in the National Institute of Advanced Studies, Indian Institute of Science Campus, Bangalore. His main research interests are : Philosophy of Science and Mathematics, Postmodernism, Phenomenology
16. Krister Segerberg, is Professor Emeritus, Uppsala University, Sweden. His current areas of interest are : Modal Logic, Doxastic Logic and Belief Revision
17. G. Venkatesh, is currently a board member of Sasken Communication Technologies Ltd. Bangalore and the Corporate Chief Technology and Strategy Officer. He is also a Visiting Professor at IIM Bangalore. His areas of interest are : Applications of game theory to strategic thinking in the technology industry, specifically the telecom and semiconductor industries, temporal logic, functional/logic programming, and applications of logic and languages to VLSI design
18. Noson Yanofsky, is Assistant Professor, Department of Computer and Information Science, Brooklyn College, New York. His research interests are : Theoretical Quantum Computing, Applied Category Theory, Quantum Complexity Theory, Categorical Universal Algebra, and Categorical Logic