2nd edition. The theory of logical consequence is central in modern logic and its applications. However, it is mostly dispersed in an abundance of often difficultly accessible papers, and rarely treated with applications in mind. This book collects the most fundamental aspects of this theory and offers the reader the basics of its applications in computer science, artificial intelligence, and cognitive science, to name but the most important fields where this notion finds its many applications.

The -logic of Terwijn is a variant of first-order logic with the same syntax in which the models are equipped with probability measures and the quantifier is interpreted as ‘there exists a set A of a measure such that for each,...’. Previously, Kuyper and Terwijn proved that the general satisfiability and validity problems for this logic are, i) for rational, respectively -complete and -hard, and ii) for, respectively decidable and -complete. The adjective ‘general’ here means ‘uniformly over all languages’. We (...) extend these results in the scenario of finite models. In particular, we show that the problems of satisfiability and validity with respect to finite models in E-logic are, i) for rational, respectively -complete and -complete, and ii) for, respectively decidable and -complete. Although partial results toward the countable case are also achieved, the computability of E-logic over countable models still remains largely unsolved. In addition, most o... (shrink)