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Categorical Logic and Type Theory
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Introduction to Coalgebra
An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.
Categorical Quantum Models and Logics
This dissertation studies the logic behind quantum physics, using category theory as the principal tool and conceptual guide. To do so, principles of quantum mechanics are modeled categorically. These categorical quantum models are justified by an embedding into the category of Hilbert spaces, the traditional formalism of quantum physics. In particular, complex numbers emerge without having been prescribed explicitly. Interpreting logic in such categories results in orthomodular property lattices, and furthermore provides a natural setting to consider quantifiers. Finally, topos theory, incorporating categorical logic in a refined way, lets one study a quantum system as if it were classical, in particular leading to a novel mathematical notion of quantum-
Logic and the Modalities in the Twentieth Century
Logic and the Modalities in the Twentieth Century is an indispensable research tool for anyone interested in the development of logic, including researchers, graduate and senior undergraduate students in logic, history of logic, mathematics, history of mathematics, computer science and artificial intelligence, linguistics, cognitive science, argumentation theory, philosophy, and the history of ideas.This volume is number seven in the eleven volume Handbook of the History of Logic. It concentrates on the development of modal logic in the 20th century, one of the most important undertakings in logic's long history. Written by the leading researchers and scholars in the field, the volume explor...
Practical Foundations of Mathematics
Practical Foundations collects the methods of construction of the objects of twentieth-century mathematics. Although it is mainly concerned with a framework essentially equivalent to intuitionistic Zermelo-Fraenkel logic, the book looks forward to more subtle bases in categorical type theory and the machine representation of mathematics. Each idea is illustrated by wide-ranging examples, and followed critically along its natural path, transcending disciplinary boundaries between universal algebra, type theory, category theory, set theory, sheaf theory, topology and programming. Students and teachers of computing, mathematics and philosophy will find this book both readable and of lasting value as a reference work.
Verification of Object-Oriented Software. The KeY Approach
The ultimate goal of program verification is not the theory behind the tools or the tools themselves, but the application of the theory and tools in the software engineering process. Our society relies on the correctness of a vast and growing amount of software. Improving the software engineering process is an important, long-term goal with many steps. Two of those steps are the KeY tool and this KeY book.
Formal Methods for Components and Objects
Largeandcomplexsoftwaresystemsprovidethenecessaryinfrastuctureinall- dustries today. In order to construct such large systems in a systematic manner, the focus in the development methodologies has switched in the last two decades from functional issues to structural issues: both data and functions are enc- sulated into software units that are integrated into large systems by means of various techniques supporting reusability and modi?ability. This encapsulation principleisessentialtoboththeobject-orientedandthemorerecentcompone- based sofware engineering paradigms. Formalmethodshavebeenappliedsuccessfullytotheveri?cationofmedi- sized programs in protocol and hardware design. However, their a...
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Creolization and Contraband
DIVWhen Curaçao came under Dutch control in 1634, the small island off South America's northern coast was isolated and sleepy. The introduction of increased trade (both legal and illegal) led to a dramatic transformation, and Curaçao emerged as a major hub within Caribbean and wider Atlantic networks. It would also become the commercial and administrative seat of the Dutch West India Company in the Americas. The island's main city, Willemstad, had a non-Dutch majority composed largely of free blacks, urban slaves, and Sephardic Jews, who communicated across ethnic divisions in a new creole language called Papiamentu. For Linda M. Rupert, the emergence of this creole language was one of...
