After the success of his first publication A Chordal Concept for Jazz Guitar, renowned Australian guitarist Peter O'Mara explores the depths of jazz improvisation from a guitarist's point of view. This new book covers a wide variety of topics---scales, intervals, triads, non-tertial triads, four-note structures, five-note structures (pentatonic scales), as well as useful practical exercises. Fourteen modes and their applications are covered in detail. The book also includes a play-a-long CD, MIDI files, as well as a demonstration CD. A must for the contemporary jazz guitarist! Titles: Introduction * Triads * Four-Note Structures * Diatonic Relationships * Examples and Modal Exercises * Ezam * The Wheel * About the Author.

Nicholas F. Stang explores Kant's theory of possibility, from the precritical period of the 1750-60s to the Critical system initiated by the Critique of Pure Reason in 1781. He argues that the key to understanding the relationship between these periods lies in Kant's reorientation of an ontological question towards a transcendental approach.

This book develops a novel generalization of possible world semantics, called ‘world line semantics’, which recognizes worlds and links between world-bound objects (world lines) as mutually independent aspects of modal semantics. Addressing a wide range of questions vital for contemporary debates in logic and philosophy of language and offering new tools for theoretical linguistics and knowledge representation, the book proposes a radically new paradigm in modal semantics. This framework is motivated philosophically, viewing a structure of world lines as a precondition of modal talk. The author provides a uniform analysis of quantification over individuals (physical objects) and objects of thought (intentional objects). The semantic account of what it means to speak of intentional objects throws new light on accounts of intentionality and singular thought in the philosophy of mind and offers novel insights into the semantics of intensional transitive verbs.

What is possible and why? What is the difference between the merely possible and the actual? In Kants Modal Metaphysics Nicholas Stang examines Kants lifelong engagement with these questions and their role in his philosophical development. This is the first book to trace Kants theory of possibility all theway from the so-called pre-Critical writings of the 1750s and 1760s to the Critical system of philosophy inaugurated by the Critique of Pure Reason in 1781. Stang argues that the key to understanding both the change and the continuity between Kants pre-Critical and Critical theory of possibility is his transformation of the ontological question about possibility-what is it for a being to be possible?-into a question in transcendental philosophy-what is it to represent an object as possible? The first half of Kants Modal Metaphysics explores Kants pre-Critical theory of possibility, including his answer to the ontological question about the nature of possibility, his rejection of the traditional ontological argument for the existence of God, and his own argument that God must exist to ground all possibility. The second half examines why Kant reoriented his theory of possibility around the transcendental question, what this question means, and how Kant answered it in the Critical philosophy. Stang shows that, despite this reorientation, Kants basic scheme for thinking about possibility remains constant from the pre-Critical period through the Critical system. What had been an ontological theory of possible being is reinterpreted, in the Critical system, as a theory of how we must represent possible objects, given the nature of our intellect.

Possible Worlds presents the first up-to-date and comprehensive examination of one of the most important topics in metaphysics. John Divers considers the prevalent philosophical positions, including realism, antirealism and the work of important writers on possible worlds such as David Lewis, evaluating them in detail.

Highlighting Hegel's conceptual realism Hoffmann focuses on an undervalued move in his dialectic: inversion (μεταβολή). Easily proving completeness for Kant's table of categories, Hoffmann shows how metabolic dialectic substantiates Hegel's claim for his Logic: it is indeed the science of absolute form!

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects.To study the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery.We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics.The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources.The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well.Key Features:• Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science• Written by internationally leading researchers in the field of pure and applied logic• Combines mathematical theory of modal logic and applications in artificial intelligence and computer science• Numerous open problems for further research• Well illustrated with pictures and tables