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Introduction to Coalgebra
An accessible introduction to coalgebra, with clear mathematical explanations and numerous examples and exercises.
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...
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-
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.
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...
House documents
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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.
Campbell Vs. Morey
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Algebra and Coalgebra in Computer Science
In April 2004, after one year of intense debate, CMCS, the International Workshop on Coalgebraic Methods in Computer Science, and WADT, the Workshop on Al- braic Development Techniques, decided to join their forces and reputations into a new high-level biennial conference. CALCO, the Conference on Algebra and Co- gebra in Computer Science, was created to bring together researchers and practit- ners to exchange new results related to foundational aspects, and both traditional and emerging uses of algebras and coalgebras in computer science. A steering committee was put together by merging those of CMCS and WADT: Jiri Adamek, Ataru Na- gawa, Michel Bidoit, José Fiadeiro (co-chair), Hans-Peter...
