Kategoria BISAC: Mathematics >> Logic

This book argues that languages are composed of sets of signs, rather than strings . This notion, first posited by de Saussure in the early 20^th century, has for decades been neglected by linguists, particularly following Chomsky s heavy critiques of the 1950s. Yet since the emergence of formal semantics in the 1970s, the issue of compositionality has gained traction in the theoretical debate, becoming a selling point for linguistic theories.

Yet the concept of compositionality itself remains ill-defined, an issue this book addresses. Positioning compositionality as a...

The theory presented in this book is developed constructively, is based on a few axioms encapsulating the notion of objects (points and sets) being apart, and encompasses both point-set topology and the theory of uniform spaces. While the classical-logic-based theory of proximity spaces provides some guidance for the theory of apartness, the notion of nearness/proximity does not embody enough algorithmic information for a deep constructive development. The use of constructive (intuitionistic) logic in this book requires much more technical ingenuity than one finds in classical proximity...

The chief purpose of the book is to present, in detail, a compilation of proofs of the Cantor-Bernstein Theorem (CBT) published through the years since the 1870's. Over thirty such proofs are surveyed.

The book comprises five parts. In the first part the discussion covers the role of CBT and related notions in the writings of Cantor and Dedekind. New views are presented, especially regarding the general proof of CBT obtained by Cantor, his proof of the Comparability Theorem, the ruptures in the Cantor-Dedekind correspondence and the origin of Dedekind's proof of CBT.

The second...

The topic of this book is the following optimisation problem: given a set of discrete variables and a set of functions, each depending on a subset of the variables, minimise the sum of the functions over all variables. This fundamental research problem has been studied within several different contexts of discrete mathematics, computer science and artificial intelligence under different names: Min-Sum problems, MAP inference in Markov random fields (MRFs) and conditional random fields (CRFs), Gibbs energy minimisation, valued constraint satisfaction problems (VCSPs), and, for two-state...

In this era of heterogeneous and distributed data sources, ranging from semistructured documents to knowledge about coordination processes or workflows, logic provides a rich set of tools and techniques with which to address the questions of how to represent, query and reason about complex data.

This book provides a state-of-the-art overview of research on the application of logic-based methods to information systems, covering highly topical and emerging fields: XML programming and querying, intelligent agents, workflow modeling and verification, data integration, temporal and...

Thisvolume examines the limitations of mathematical logic and proposes a new approach to logic intended to overcome them. To this end, the book compares mathematical logic with earlier views of logic, both in the ancient and in the modern age, including those of Plato, Aristotle, Bacon, Descartes, Leibniz, and Kant. From the comparison it is apparent that a basic limitation of mathematical logic is that it narrows down the scope of logic confining it to the study of deduction, without providing tools for discovering anything new. As a result, mathematical logic has had little impact on...