This book is well known for its proof that many mathematical systems - including lattice theory and closure algebras - are undecidable. It consists of three treatises from one of the greatest logicians of all time: "A General Method in Proofs of Undecidability," "Undecidability and Essential Undecidability in Mathematics," and "Undecidability of the Elementary Theory of Groups.".

Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...

A textbook on modal logic, intended for readers already acquainted with the elements of formal logic, containing nearly 500 exercises. Brian F. Chellas provides a systematic introduction to the principal ideas and results in contemporary treatments of modality, including theorems on completeness and decidability. Illustrative chapters focus on deontic logic and conditionality. Modality is a rapidly expanding branch of logic, and familiarity with the subject is now regarded as a necessary part of every philosopher's technical equipment. Chellas here offers an (...) up-to-date and reliable guide essential for the student. (shrink)

This comprehensive anthology draws together classic and contemporary readings by leading philosophers on epistemology. Ideal for any philosophy student, it will prove essential reading for epistemology courses, and is designed to complement Robert Audi's textbook _Epistemology: A Contemporary Introduction_. Themes covered include, perception, memory, inductive inference, reason and the a priori, the architecture of knowledge, skepticism, the analysis of knowledge, testimony. Each section begins with an introductory essay, guiding students into the topic. Includes articles by: Russell, Hume, Berkeley, Malcolm, Quine, (...) Carnap, J.L. Austin, Pollock, Nozick, Putnam, G.E. Moore, Huemer, Reid, Plato, BonJour, Coady, Carroll, Fumerton, Edwards, Foster, Howson, Urbach, Stove, Empiricus, Oakley, Alston, Gettier, Clark, Goldman, Lehrer, Paxson, DeRose, Dretske, Klein and Chisholm. (shrink)

G. E. Moore observed that to assert, 'I went to the pictures last Tuesday but I don't believe that I did' would be 'absurd'. Over half a century later, such sayings continue to perplex philosophers. In the definitive treatment of the famous paradox, Green and Williams explain its history and relevance and present new essays by leading thinkers in the area.

In _Modal Logic for Open Minds,_ Johan van Benthem provides an up-to-date introduction to the field of modal logic, outlining its major ideas and exploring the numerous ways in which various academic fields have adopted it. Van Benthem begins with the basic theories of modal logic, semantics, bisimulation, and axiomatics, and also covers more advanced topics, such as expressive power and computational complexity. The book then moves to a wide range of applications, including new developments in information flow, intelligent agency, (...) and games. Taken together, the chapters show modal logic at the crossroads of philosophy, mathematics, linguistics, computer science, and economics. Most of the chapters are followed by exercises, making this volume ideal for undergraduate and graduate students in philosophy, computer science, symbolic systems, cognitive science, and linguistics. (shrink)

This modern, advanced textbook reviews modal logic, a field which caught the attention of computer scientists in the late 1970's.

In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... , (...) the operators v (or), ~ (not) and □ (necessarily), the universal quantifier (p), p a propositional variable, and brackets ( and ). The formulas of L are then defined in the usual way. (shrink)

I am interested in extending modal calculi by adding propositional quantifiers, given by the rules for quantifier introduction: provided that p does not occur free in A.