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| Author | : Allen L. Mann |
| Publisher | : Cambridge University Press |
| Total Pages | : 215 |
| Release | : 2011-05-05 |
| Genre | : Mathematics |
| ISBN | : 1139495917 |
Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic, an exciting logical formalism at the interface of logic and game theory. It is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic.
| Author | : Jouko Väänänen |
| Publisher | : Cambridge University Press |
| Total Pages | : 52 |
| Release | : 2007-05-10 |
| Genre | : Mathematics |
| ISBN | : 1139465155 |
Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets - but what is the logic of dependence? This book is the first to carry out a systematic logical study of this important concept, giving on the way a precise mathematical treatment of Hintikka's independence friendly logic. Dependence logic adds the concept of dependence to first order logic. Here the syntax and semantics of dependence logic are studied, dependence logic is given an alternative game theoretic semantics, and results about its complexity are proven. This is a graduate textbook suitable for a special course in logic in mathematics, philosophy and computer science departments, and contains over 200 exercises, many of which have a full solution at the end of the book. It is also accessible to readers, with a basic knowledge of logic, interested in new phenomena in logic.
| Author | : Jouko Va{diaer}a{diaer}na{diaer}nen |
| Publisher | : |
| Total Pages | : 225 |
| Release | : 2007 |
| Genre | : First-order logic |
| ISBN | : 9780511286131 |
A systematic logical study of dependence also providing a precise treatment of independence friendly logic.
| Author | : Allen Lawrence Mann |
| Publisher | : |
| Total Pages | : 208 |
| Release | : 2011 |
| Genre | : First-order logic |
| ISBN | : 9781107213395 |
Bringing together over twenty years of research, this book gives a complete overview of independence-friendly logic. It emphasizes the game-theoretical approach to logic, according to which logical concepts such as truth and falsity are best understood via the notion of semantic games. The book pushes the paradigm of game-theoretical semantics further than the current literature by showing how mixed strategies and equilibria can be used to analyze independence-friendly formulas on finite models. The book is suitable for graduate students and advanced undergraduates who have taken a course on first-order logic. It contains a primer of the necessary background in game theory, numerous examples and full proofs.
| Author | : J. F. A. K. van Benthem |
| Publisher | : Amsterdam University Press |
| Total Pages | : 363 |
| Release | : 2007 |
| Genre | : Philosophy |
| ISBN | : 9053563563 |
Traditionally, logic has dealt with notions of truth and reasoning. In the past several decades, however, research focus in logic has shifted to the vast field of interactive logic—the domain of logics for both communication and interaction. The main applications of this move are logical approaches to games and social software; the wealth of these applications was the focus of the seventh Augustus de Morgan Workshop in November 2005. This collection of papers from the workshop serves as the initial volume in the new series Texts in Logics and Games—touching on research in logic, mathematics, computer science, and game theory. “A wonderful demonstration of contemporary topics in logic.”—Wiebe van der Hoek, University of Liverpool
| Author | : Shahid Rahman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 618 |
| Release | : 2009-03-15 |
| Genre | : Philosophy |
| ISBN | : 1402028083 |
The first volume in this new series explores, through extensive co-operation, new ways of achieving the integration of science in all its diversity. The book offers essays from important and influential philosophers in contemporary philosophy, discussing a range of topics from philosophy of science to epistemology, philosophy of logic and game theoretical approaches. It will be of interest to philosophers, computer scientists and all others interested in the scientific rationality.
| Author | : Jaakko Hintikka |
| Publisher | : Cambridge University Press |
| Total Pages | : 308 |
| Release | : 1998-04-28 |
| Genre | : Mathematics |
| ISBN | : 9780521624985 |
This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.
| Author | : Esa. Saarinen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 400 |
| Release | : 2007-11-05 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 140204108X |
This book is a collection of studies applying game-theoretical concepts and ideas to analysing the semantics of natural language and some formal languages. The bulk of the book consists of several papers by Hintikka, Carlson and Saarinen and discusses several of the central problems of the semantics of natural language. The topics covered are the semantics of natural language quantifiers, conditionals, pronouns and anaphora more generally. Hintikka’s famous essay presenting examples of "branching quantifier structures" in English, as well as one formulating his "any-every thesis", are included. The book also includes Hintikka’s closely argued philosophical discussion of the relationships between the new semantical games with the language games of Wittgenstein. Other papers apply the game-theoretical approach to formal languages including tense logics and tense anaphora (Saarinen), deontic logic and Ross’ paradox (Hintikka), and usual predicate logic (Rantala). The latter amounts to an explication of the "impossible possible" worlds as is shown in Hintikka’s concluding paper.
