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132
Towards Automated Derivation in the Theory of Allegories
, 2008
"... 2.1 Graphs representing the terms 1 n xxO and dom(x)....... 8 2.2 Sample graphs representing the basic graphs 1, 2x, and the operations gllg2, gIilg2, gl and br(g) in PLIx. The corresponding terms are listed to the left of each graph...... 9 2.3 Sample terms in ALL with their respective graphs in ..."
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2.1 Graphs representing the terms 1 n xxO and dom(x)....... 8 2.2 Sample graphs representing the basic graphs 1, 2x, and the operations gllg2, gIilg2, gl and br(g) in PLIx. The corresponding terms are listed to the left of each graph...... 9 2.3 Sample terms in ALL with their respective graphs
On a Graph Calculus for Algebras of Relations?
"... Abstract. We present a sound and complete logical system for deriving inclusions between graphs from inclusions between graphs, taken as hypotheses. Graphs provide a natural tool for expressing relations and reasoning about them. Here we extend this system to a sound and complete one to cope with ..."
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Abstract. We present a sound and complete logical system for deriving inclusions between graphs from inclusions between graphs, taken as hypotheses. Graphs provide a natural tool for expressing relations and reasoning about them. Here we extend this system to a sound and complete one to cope
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 116 (14 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of floating point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We describe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the `Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally,...
Abstract and Concrete Categories. The Joy of Cats
, 2004
"... Contemporary mathematics consists of many different branches and is intimately related to various other fields. Each of these branches and fields is growing rapidly and is itself diversifying. Fortunately, however, there is a considerable amount of common ground — similar ideas, concepts, and constr ..."
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Cited by 107 (0 self)
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Contemporary mathematics consists of many different branches and is intimately related to various other fields. Each of these branches and fields is growing rapidly and is itself diversifying. Fortunately, however, there is a considerable amount of common ground — similar ideas, concepts, and constructions. These provide a basis for a general theory of structures.
The purpose of this book is to present the fundamental concepts and results of such a theory, expressed in the language of category theory — hence, as a particular branch of mathematics itself. It is designed to be used both as a textbook for beginners and as a reference source. Furthermore, it is aimed toward those interested in a general theory of structures, whether they be students or researchers, and also toward those interested in using such a general theory to help with organization and clarification within a special field. The only formal prerequisite for the reader is an elementary knowledge of set theory.
Formal Methods for Interactive Systems
, 1991
"... This material is copyright. You must include this page with any portion of the book. Please refer to book web site for distribution conditions. Please note that as the book has been retypeset for electronic distribution, page numbers may difer slightly from the original. CONTENTS Preface ..."
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Cited by 90 (21 self)
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This material is copyright. You must include this page with any portion of the book. Please refer to book web site for distribution conditions. Please note that as the book has been retypeset for electronic distribution, page numbers may difer slightly from the original. CONTENTS Preface
Algebraizations Of Quantifier Logics, An Introductory Overview
, 1991
"... . This work is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics as well as those propositional logics (like modal logics) in the semantics of which theories of relations play an essential role. ..."
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Cited by 45 (4 self)
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. This work is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics as well as those propositional logics (like modal logics) in the semantics of which theories of relations play an essential role. This work has a survey character, too. The most frequently used algebras like cylindric, relation, polyadic, and quasipolyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some directions we tried to give an overview of the most recent results and research trends, too. Contents 1. Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2 2. Gett...
A crash course in arrow logic
 in Arrow Logics and Multimodal Logics
, 1996
"... Overview This contribution gives a short introduction to arrow logic. We start by explaining the basic idea underlying arrow logic and the motivation for studying it (sections 1 and 2). We discuss some elementary duality theory between arrow logic and the algebraic theory of binary relations (sectio ..."
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Cited by 30 (1 self)
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(section 3). In the sections 4 and 5 we give a brief survey of the theory that has been developed on the semantics (de nability), axiomatics and decidability ofvarious systems of arrow logic. We brie y describe some closely related formalisms and some extensions and reducts of arrow logic in section 6. We
Tile Logic for Synchronized Rewriting of Concurrent Systems
, 1999
"... Tile logic is a framework to reason about the dynamic evolution of concurrent systems in a modular way. It extends rcwritig logic (in the unconditional case) by adding rewriting synchronization and side effects. This dissertation concerns both theoretical and implementation issues of tile models of ..."
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Cited by 38 (19 self)
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Tile logic is a framework to reason about the dynamic evolution of concurrent systems in a modular way. It extends rcwritig logic (in the unconditional case) by adding rewriting synchronization and side effects. This dissertation concerns both theoretical and implementation issues of tile models of computation where the mathematical structures representing cofi'guratios (i.e., system states) and obscrvatios (i.e., observable actions) rely on the same common auxiliary structure (e.g., for tupling, projecting, etc.).
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