This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair...

Noam Chomsky is one of the most influential thinkers of our time, yet his views are often misunderstood. In this previously unpublished series of interviews, Chomsky discusses his iconoclastic and important ideas concerning language, human nature and politics. In dialogue with James McGilvray, Professor of Philosophy at McGill University, Chomsky takes up a wide variety of topics – the nature of language, the philosophies of language and mind, morality and universality, science and common ...

This book presents the technique of visual logic thinking. The technique consists of separate consecutive parts, which as whole become "skeleton" for information processing with following topics: mnemonic technique of memorization of events and dialogues, visual analysis of events in space and time, visualization of semantic connections and taxonomical groups of abstract essences, estimation of probabilities, essences sorting, rules for work in mixes of disciplines, and also practical meth...

The algebra of logic was founded by George Boole (1815-1864); it was developed and perfected by Ernst Schroder (1841-1902) The fundamental laws of this calculus were devised to express the principles of reasoning, the laws of thought But this calculus may be considered from the purely formal point of view, which is that of mathematics, as an algebra based upon certain principles arbitrarily laid down It belongs to the realm of philosophy to decide whether, and in what measure, this calculu...

This book emphasizes the role of symmetry and presents as many viewpoints as possible of an important phenomenon — the functional equation of the associated zeta-function. It starts from the basics before warping into the space of new interest; from the ground state to the excited state. For example, the celebrated Gauss quadratic reciprocity law is proved in four independent ways, which are in some way or other dependent on the functional equation. The proofs rest on finite fields, repres...

This book is written for undergraduates who wish to learn some basic results in analytic number theory. It covers topics such as Bertrand's Postulate, the Prime Number Theorem and Dirichlet's Theorem of primes in arithmetic progression.The materials in this book are based on A Hildebrand's 1991 lectures delivered at the University of Illinois at Urbana-Champaign and the author's course conducted at the National University of Singapore from 2001 to 2008.

Generative Grammar presents a substantial contribution to the field of linguistics in drawing together for the first time the author's most significant work on the theory of generative grammar.The essays collected here display Freidin's role in moving the theory forward in terms of new proposals, and analyse the efforts to understand the evolution and history of the theory by careful investigation of how and why it has changed over the years.

Collected for the first time in a single volume, these essays and articles by Naoki Fukui form an outline of some of the most significant and formative contributions to syntactic theory. Focusing particularly on the typological differences between English/type language and Japanese/type languages, Fukui examines the abstract parameters that both link and divide them. Linguistic universals are considered in the light of cross-linguistic variation and typological (parametric) differences are...

This volume on the semantic complexity of natural language explores the question why some sentences are more difficult than others. While doing so, it lays the groundwork for extending semantic theory with computational and cognitive aspects by combining linguistics and logic with computations and cognition.Quantifier expressions occur whenever we describe the world and communicate about it. Generalized quantifier theory is therefore one of the basic tools of linguistics today, stu...

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophe...

This second edition of the Handbook of Philosophical Logic reflects great changes in the landscape of philosophical logic since the first edition. It gives readers an idea of that landscape and its relation to computer science and formal language and artificial intelligence. It shows how the increased demand for philosophical logic from computer science and artificial intelligence and computational linguistics accelerated the development of the subject directly and indirectly. This develop...

Parameters of linguistic variation were originally conceived, within the chomskyan Principles and Parameters Theory, as UG-determined options that were associated with grammatical principles and had a rich deductive structure. This characterization of parametric differences among languages has changed significantly over the years, especially so with the advent of Minimalism. This book collects a representative sample of current generative research on the status, origin and size of paramete...