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A High-Performance Logical Framework -- All About Maude : How to Specify, Program, and Verify Systems in Rewriting Logic
This book gives a comprehensive account of Maude, a language and system based on rewriting logic. Many examples are used throughout the book to illustrate the main ideas and features of Maude, and its many possible uses. Maude modules are rewrite theories. Computation with such modules is - cient deduction by rewriting. Because of its logical basis and its initial model semantics,aMaude module defines a precise mathematical model.This means that Maude and its formal tool environment can be used in three, mutually reinforcing ways: • as a declarative programming language; • as an executable formal specification language; and • as a formal verification system. Maude’s rewriting logic is simple, yet very expressive. This gives Maude good representational capabilities as a semantic framework to formally represent a wide range of systems, including models of concurrency, distributed al- rithms, network protocols, semantics of programming languages, and models of cell biology. Rewriting logic is also an expressive universal logic,making Maude a fiexible logical framework in which many difierent logics and - ference systems can be represented and mechanized. This makes Maude a useful metatool to build many other tools, including those in its own formal tool environment. Thanks to the logic’s simplicity and the use of advanced semi-compilation techniques, Maude has a high-performance implementation, making it competitive with other declarative programming languages.
Logica Universalis : Towards a General Theory of Logic
Modern logic has been intimately connected with algebra since its origins in figures such as Boole, De Morgan, and Peirce. But while universal algebra is a long recognized field, universal logic has only recently been named as such. This is perhaps because classical logic was until relatively recently taken by many as the "one true logic". But with the proliferation of special purpose non-classical logics in recent years, universal logic is clearly a field whose time has come. This book contains many excellent papers demonstrating the value of this approach.
Logica Universalis : Towards a General Theory of Logic
Signifies the arrival of a new renaissance in logic, a new revival not only of logic, but of the vision of logic as a unifying tool for science as a whole, including mathematics, physics, cosmology, computer science and AI. The book and the vision behind it give logic, conceived as a scientific study of rationality, new unifying power, new perspectives, and new horizons.Universal Logic is not a new logic, but a general theory of logics, considered as mathematical structures. The name was introduced about ten years ago, but the subject is as old as the beginning of modern logic: Alfred Tarski and other Polish logicians such as Adolf Lindenbaum developed a general theory of logics at the end of the 1920s based on consequence operations and logical matrices. The subject was revived after the flowering of thousands of new logics during the last thirty years: there was a need for a systematic theory of logics to put some order in this chaotic multiplicity.
Completeness theory for propositional logics
Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been de?ned in literature. We shallconcentrateonthesevariants,andaspects,of completenesswhicharede?ned in propositional logic. Completeness means the possibility of getting all correct and reliable sc- mata of inference by use of logical methods. The word ‘all’, seemingly neutral, is here a crucial point of distinction. Assuming the de?nition as given by E. Post we get, say, a global notion of completeness in which the reliability refers only to syntactic means of logic and outside the correct schemata of inference there are only inconsistent ones. It is impossible, however, to leave aside local aspects of the notion when we want to make it relative to some given or invented notion of truth. Completeness understood in this sense is the adequacy of logic in relation to some semantics, and the change of the logic is accompanied by the change of its semantics.
