Formal analysis is the study of formal power series, formal Laurent series, formal root series, and other formal series or formal functionals. This book is the first comprehensive presentation of the topic that systematically introduces formal analysis, including its algebraic, analytic, and topological structure, along with various applications.

Introduction to Art: Design, Context, and Meaning offers a deep insight and comprehension of the world of Art. Contents: What is Art? The Structure of Art Significance of Materials Used in Art Describing Art - Formal Analysis, Types, and Styles of Art Meaning in Art - Socio-Cultural Contexts, Symbolism, and Iconography Connecting Art to Our Lives Form in Architecture Art and Identity Art and Power Art and Ritual Life - Symbolism of Space and Ritual Objects, Mortality, and Immortality Art and Ethics

In Art and Representation, John Willats presents a radically new theory of pictures. To do this, he has developed a precise vocabulary for describing the representational systems in pictures: the ways in which artists, engineers, photographers, mapmakers, and children represent objects. His approach is derived from recent research in visual perception and artificial intelligence, and Willats begins by clarifying the key distinction between the marks in a picture and the features of the scene that these marks represent. The methods he uses are thus closer to those of a modern structural linguist or psycholinguist than to those of an art historian. Using over 150 illustrations, Willats analyzes the representational systems in pictures by artists from a wide variety of periods and cultures. He then relates these systems to the mental processes of picture production, and, displaying an impressive grasp of more than one scholarly discipline, shows how the Greek vase painters, Chinese painters, Giotto, icon painters, Picasso, Paul Klee, and David Hockney have put these systems to work. But this book is not only about what systems artists use but also about why artists from different periods and cultures have used such different systems, and why drawings by young children look so different from those by adults. Willats argues that the representational systems can serve many different functions beyond that of merely providing a convincing illusion. These include the use of anomalous pictorial devices such as inverted perspective, which may be used for expressive reasons or to distance the viewer from the depicted scene by drawing attention to the picture as a painted surface. Willats concludes that art historical changes, and the developmental changes in children's drawings, are not merely arbitrary, nor are they driven by evolutionary forces. Rather, they are determined by the different functions that the representational systems in pictures can serve. Like readers of Ernst Gombrich's famous Art and Illusion (still available from Princeton University Press), on which Art and Representation makes important theoretical advances, or Rudolf Arnheim's Art and Visual Perception, Willats's readers will find that they will never again return to their old ways of looking at pictures.

The book provides a gentle introduction and definition of the denotational-based abstract interpretation method. The book demonstrates how the above method of formal analysis can be used, not only to address the security of systems, but other more general and interesting properties related to the testing, mutating and semantic ambiguity resolution of protocols. The book presents three case studies, all related to current complex protocols and standards used in industry, particularly in the context of IoT and Industry 4.0.

This book describes an accurate analysis technique for energy systems based on formal methods—computer-based mathematical logic techniques for the specification, validation, and verification of the systems. Correctness and accuracy of the financial, operational, and implementation analysis are of the paramount importance for the materialization of the future energy systems, such as smart grids, to achieve the objectives of cost-effectiveness, efficiency, and quality-of-service. In this regard, the book develops formal theories of microeconomics, asymptotic, and stability to support the formal analysis of generation and distribution cost, smart operations, and processing of energy in a smart grid. These formal theories are also employed to formally verify the cost and utility modeling for: Energy generation and distribution; Asymptotic bounds for online scheduling algorithms for plug-in electric vehicles; and Stability of the power converters for wind turbines. The proposed approach results in mechanized proofs for the specification, validation, and verification of corresponding smart grid problems. The formal mathematical theories developed can be applied to the formal analysis of several other hardware and software systems as well, making this book of interest to researchers and practicing engineers in a variety of power electronic fields.

Formal Concept Analysis is a field of applied mathematics based on the mathematization of concept and conceptual hierarchy. It thereby activates mathematical thinking for conceptual data analysis and knowledge processing. The underlying notion of “concept” evolved early in the philosophical theory of concepts and still has effects today. In mathematics it played a special role during the emergence of mathematical logic in the 19th century. Subsequently, however, it had virtually no impact on mathematical thinking. It was not until 1979 that the topic was revisited and treated more thoroughly. Since then, Formal Concept Analysis has fully emerged, sparking a multitude of publications for which the first edition of this textbook established itself as the standard reference in the literature, with a total of 10000+ citations. This is the second edition, revised and extended, of the textbook published originally in German (1996) and translated into English (1999), giving a systematic presentation of the mathematical foundations while also focusing on their possible applications for data analysis and knowledge processing. In times of digital knowledge processing, formal methods of conceptual analysis are gaining in importance. The book makes the basic theory for such methods accessible in a compact form, and presents graphical methods for representing concept systems that have proved themselves essential in communicating knowledge. The textbook complements each chapter with further notes, references and trends, putting the work in modern context and highlighting potential directions for further research. Additionally, the book contains an entirely new chapter on contextual concept logic, including a section on description logics and relational concept analysis. As such, it should be a valuable resource for students, instructors and researchers at the crossroads of subject areas like Applied and Discrete Mathematics, Logics, Theoretical Computer Science, Knowledge Processing, Data Science, and is meant to be used both for research and in class, as a teaching resource.

This is an analysis of complex forms of art history. It covers a broad range of approaches, presenting individual arguments, controversies and divergent perspectives. The book begins by introducing the concept of theory and explains why it is important to the practice of art history.

Formal concept analysis has been developed as a field of applied mathematics based on the mathematization of concept and concept hierarchy. It thereby allows us to mathematically represent, analyze, and construct conceptual structures. The formal concept analysis approach has been proven successful in a wide range of application fields. This book constitutes a comprehensive and systematic presentation of the state of the art of formal concept analysis and its applications. The first part of the book is devoted to foundational and methodological topics. The contributions in the second part demonstrate how formal concept analysis is successfully used outside of mathematics, in linguistics, text retrieval, association rule mining, data analysis, and economics. The third part presents applications in software engineering.

Adjectives are comparatively less well studied than the lexical categories of nouns and verbs. The present volume brings together studies in the syntax and semantics of adjectives. Four of the contributions investigate the syntax of adjectives in a variety of languages (English, French, Mandarin Chinese, Modern Hebrew, Russian, Spanish, and Serbocroatian). The theoretical issues explored include: the syntax of attributive and predicative adjectives, the syntax of nominalized adjectives and the identification of adjectives as a distinct lexical category in Mandarin Chinese. A further four contributions examine different aspects in the semantics of adjectives in English, French, and Spanish, dealing with superlatives, comparatives, and aspect in adjectives. This volume will be of interest to researchers and students in syntax, formal semantics, and language typology.

Can quantum particles be regarded as individuals, just like books, tables and people? According to the 'received' view - articulated by several physicists in the immediate aftermath of the quantum revolution - quantum physics itself tells us they cannot: quantum particles, unlike their classical counterparts, must be regarded as 'non-individuals' in some sense. However, recent work has indicated that this is not the whole story and that the theory is also consistent with theposition that such particles can be taken to be individuals, albeit at a metaphysical price.Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, the authors explore these two alternative metaphysical packages. In particular, they argue that if quantum particles are regarded as individuals, then Leibniz's famous Principle of the Identity of Indiscernibles is in fact violated. Recent discussions of this conclusion are analysed in detail and, again, the costs involved in saving the Principle are carefullyconsidered.Taking the alternative package, the authors deploy recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.Identity in Physics brings together a range of work in this area and further develops the authors' own contributions to the debate. Uniquely, as the title indicates, it situates this work in the appropriate formal, historical, and philosophical contexts.