Theo-Logic is a variation of theology, it being about not so much what man says about God, but what God speaks about Himself. Balthasar does not address the truth about God until he first reflects on the beauty of God (Glory of the Lord). Then he follows with his reflections on the great drama of our salvation and the goodness and mercy of the God who saves us (Theo-Drama). Now, in this work, he is ready to reflect on the truth that God reveals about Himself, which is not something abstract or theoretical, but rather the concrete and mysterious richness of God's being as a personal and loving God.

    Part 1, on propositional logic, is the old Introduction, but contains much new material. Part 2 is entirely new, and covers quantification and identity for all the logics in Part 1. The material is unified by the underlying theme of world semantics. All of the topics are explained clearly using devices such as tableau proofs, and their relation to current philosophical issues and debates are discussed. Students with a basic understanding of classical logic will find this book an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will also interest people working in mathematics and computer science who wish to know about the area.

    The development is mathematical; prior acquaintance with first-order logic and its semantics is assumed, and familiarity with the basic mathematical notions of set theory is required. The authors focus on the use of modal languages as tools to analyze the properties of relational structures, including their algorithmic and algebraic aspects. Applications to issues in logic and computer science such as completeness, computability and complexity are considered.

    The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some of the direct outgrowths leading to the frontiers of contemporary research. A a oegenetica approach is taken, presenting the subject in the context of its historical development. With hindsight the consequential avenues are pursued and the most elegant or accessible expositions given. With open questions and speculations provided throughout the reader should not only come to appreciate the scope and coherence of the overall enterprise but also become prepared to pursue research in several specific areas by studying the relevant sections.

    This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

    It is of particular importance to ethics. Indeed, new developments in practical reasoning promise to break through long-standing ethical and moral dilemmas. Practical reasoning also has consequences for philosophy of mind, value theory, and the social sciences. This anthology provides an overview of this important area of philosophy. Over the past two decades the field of practical reasoning has changed rapidly, with a small number of entrenched positions giving way to a healthy profusion of competing views. This book covers a broad spectrum of positions on practical reasoning--from the nihilist view that there are no legitimate forms of practical inference, and hence no such thing as practical reasoning, to inferential expressivism, which holds that our desires express commitments to arbitrarily different kinds of practical inferences (as when the desire to stay dry makes explicit the commitment to inferring the need to carry an umbrella if rain is forecast). Underlying all the contributions is the question of how one should go about determining what the legitimate forms of practical reasoning are.

    In recent years, a new approach to representing such systems, grounded in mathematical logic, has been developed within the AI knowledge-representation community.This book presents a comprehensive treatment of these ideas, basing its theoretical and implementation foundations on the situation calculus, a dialect of first-order logic. Within this framework, it develops many features of dynamical systems modeling, including time, processes, concurrency, exogenous events, reactivity, sensing and knowledge, probabilistic uncertainty, and decision theory. It also describes and implements a new family of high-level programming languages suitable for writing control programs for dynamical systems. Finally, it includes situation calculus specifications for a wide range of examples drawn from cognitive robotics, planning, simulation, databases, and decision theory, together with all the implementation code for these examples. This code is available on the book's Web site.

    By the end of this course, students will have learned all five noun declensions, some model principal parts for the four verb conjugations, three tenses, and the use of the nominative and accusative cases.

    It is a major element in theoretical computer science and has undergone a huge revival with the ever-growing importance of computer science. This text is based on a course to undergraduates and provides a clear and accessible introduction to mathematical logic. The concept of model provides the underlying theme, giving the text a theoretical coherence whilst still covering a wide area of logic. The foundations having been laid in Part 1, this book starts with recursion theory, a topic essential for the complete scientist. Then follows Godel's incompleteness theorems and axiomatic set theory. Chapter 8 provides an introduction to model theory. There are examples throughout each section, and varied selection of exercises at the end. Answers to the exercises are given in the appendix.

    Encompassing a wide range of writings, from the Book of Genesis and the classical thinkers to the work of such twentieth-century philosophers as Collingwood and McKeon, all with introductory essays by the editor, this classic anthology offers a synoptic view of the changing philosophic notions of time.

    This volume presents a definitive introduction to twenty core areas of philosophical logic including classical logic, modal logic, alternative logics and close examinations of key logical concepts.

    Learn the geography, history, symbols, and interesting facts that make each state special. Explore the U.S.A. introduces beginning readers to the United States of America through vivid images and engaging text, giving them an exciting look at the places that make up this great country. Explore the U.S.A. is a series of AV2 media enhanced books. A unique book code printed on page 2 unlocks multimedia content. These books come alive with video, audio, weblinks, slide shows, activities, hands-on experiments, and much more.

    It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.