Advances in Modal Logic, Volume 1
Edited by Marcus Kracht, Maarten de Rijke, Heinrich Wansing, and Michael Zakhary CSLI, 1998 Library of Congress BC199.M6A38 1998 | Dewey Decimal 160
Modal logic originated in philosophy as the logic of necessity and possibility. Nowadays it has reached a high level of mathematical sophistication and found many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics.
This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It offers an up-to-date perspective on the field, with contributions covering its proof theory, its applications in knowledge representation, computing and mathematics, as well as its theoretical underpinnings.
"This collection is a useful resource for anyone working in modal logic. It contains both interesting surveys and cutting-edge technical results"
--Edwin D. Mares
The Bulletin of Symbolic Logic, March 2002
Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences.
Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems.
Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.
Jesse Norman CSLI, 2006 Library of Congress BC136.N67 2006 | Dewey Decimal 160
What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In After Euclid, Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.
This exemplary volume shows how the shared interests of three different research areas can lead to significant and fruitful exchanges: six papers each very accessibly present an exciting contribution to the study and uses of algebras, diagrams, and decisions, ranging from indispensable overview papers about shared formal members to inspirational applications of formal tools to specific problems. Contributors include Pieter Adriaans, Sergei Artemov, Steven Givant, Edward Keenan, Almerindo Ojeda, Patrick Scotto di Luzio, and Edward Stabler.
Donald E. Knuth CSLI, 2011 Library of Congress QA76.9.A43K578 2011 | Dewey Decimal 005.1
This book is a French translation of seventeen papers by Donald Knuth on algorithms both in the field of analysis of algorithms and in the design of new algorithms. They cover fundamental concepts and techniques and numerous discrete problems such as sorting, searching, data compression, theorem-proving, and cryptography, as well as methods for controlling errors in numerical computations.
The age of the Baroque—a time when great strides were made in science and mathematics—witnessed the construction of some of the world's most magnificent buildings. What did the work of great architects such as Bernini, Blondel, Guarini, and Wren have to do with Descartes, Galileo, Kepler, Desargues, and Newton? Here, George Hersey explores the ways in which Baroque architecture, with its dramatic shapes and playful experimentation with classical forms, reflects the scientific thinking of the time. He introduces us to a concept of geometry that encompassed much more than the science we know today, one that included geometrics (number and shape games), as well as the art of geomancy, or magic and prophecy using shapes and numbers.
Hersey first concentrates on specific problems in geometry and architectural design. He then explores the affinities between musical chords and several types of architectural form. He turns to advances in optics, such as artificial lenses and magic lanterns, to show how architects incorporated light, a heavenly emanation, into their impressive domes. With ample illustrations and lucid, witty language, Hersey shows how abstract ideas were transformed into visual, tactile form—the epicycles of the cosmos, the sexual mystique surrounding the cube, and the imperfections of heavenly bodies. Some two centuries later, he finds that the geometric principles of the Baroque resonate, often unexpectedly, in the work of architects such as Frank Lloyd Wright and Le Corbusier. A discussion of these surprising links to the past rounds out this brilliant reexamination of some of the long-forgotten beliefs and practices that helped produce some of Europe's greatest masterpieces.
This report addresses two questions: first, whether the spatial distribution of the American electorate has become more geographically clustered over the last 40 years with respect to party voting and socioeconomic attributes; and second, whether this clustering process has contributed to rising polarization in the U.S. House of Representatives.
Paul Lockhart Harvard University Press, 2017 Library of Congress QA115.L713 2017 | Dewey Decimal 513
Paul Lockhart reveals arithmetic not as the rote manipulation of numbers but as a set of ideas that exhibit the surprising behaviors usually reserved for higher branches of mathematics. In this entertaining survey, he explores the nature of counting and different number systems—Western and non-Western—and weighs the pluses and minuses of each.
Conceived by Johan van Benthem and Yde Venema, arrow logic started as an attempt to give a general account of the logic of transitions. The generality of the approach provided a wide application area ranging from philosophy to computer science. The book gives a comprehensive survey of logical research within and around arrow logic. Since the natural operations on transitions include composition, inverse and identity, their logic, arrow logic can be studied from two different perspectives, and by two (complementary) methodologies: modal logic and the algebra of relations. Some of the results in this volume can be interpreted as price tags. They show what the prices of desirable properties, such as decidability, (finite) axiomatisability, Craig interpolation property, Beth definability etc. are in terms of semantic properties of the logic. The research program of arrow logic has considerably broadened in the last couple of years and recently also covers the enterprise to explore the border between decidable and undecidable versions of other applied logics. The content of this volume reflects this broadening. The editors included a number of papers which are in the spirit of this generalised research program.