This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.

    Prolog is different, but not that different. Elegance is not optional. These are the themes that unify Richard O'Keefe's very personal statement on how Prolog programs should be written. The emphasis in The "Craft of Prolog" is on using Prolog effectively. It presents a loose collection of topics that build on and elaborate concepts learned in a first course. These may be read in any order following the first chapter, "Basic Topics in Prolog," which provides a basis for the rest of the material in the book.Richard A. O'Keefe is Lecturer in the Department of Computer Science at the Royal Melbourne Institute of Technology. He is also a consultant to Quintus Computer Systems, Inc.Contents: Basic Topics in Prolog. Searching. Where Does the Space Go? Methods of Programming. Data Structure Design. Sequences. Writing Interpreters. Some Notes on Grammar Rules. Prolog Macros. Writing Tokenisers in Prolog. All Solutions.

    The perfect introductory textbook, this simplified study of logic prepares readers to reason thoughtfully and to spot illogic in an argument.

    Aimed at philosophers of logic, set theory and mathematics, this philosophical treatise argues that the notion of part and whole - the theory of mereology - has application to classes because of one-membered "singleton" subclasses, thus resulting in a reconception of set theory.

    Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for computer scientists. But even this is not precise. Within computer science formal logic turns up in a number of areas, from pro gram verification to logic programming to artificial intelligence. This book is intended for computer scientists interested in automated theo rem proving in classical logic. To be more precise yet, it is essentially a theoretical treatment, not a how-to book, although how-to issues are not neglected. This does not mean, of course, that the book will be of no interest to philosophers or mathematicians. It does contain a thorough presentation of formal logic and many proof techniques, and as such it contains all the material one would expect to find in a course in formal logic covering completeness but, not incompleteness issues. The first item to be addressed is, What are we talking about and why are we interested in it? We are primarily talking about truth as used in mathematical discourse, and our interest in it is, or should be, self evident. Truth is a semantic concept, so we begin with models and their properties. These are used to define our subject."

    One such formalism is the type theory developed by Per Martin-L f. Well suited as a theory for program construction, it makes possible the expression of both specifications and programs within the same formalism. Furthermore, the proof rules can be used to derive a correct program from a specification as well as to verify that a given program has a certain property. This book contains a thorough introduction to type theory, with information on polymorphic sets, subsets, monomorphic sets, and a full set of helpful examples.