This paper discusses applications of a formal set-theoretic foundation for fuzzy set theory [23] to problems of approximate and uncertain reasoning, and also looks at other formalisms, such as the classical Alternativ...
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This paper discusses applications of a formal set-theoretic foundation for fuzzy set theory [23] to problems of approximate and uncertain reasoning, and also looks at other formalisms, such as the classical Alternative Set Theory 139) and its Intuitionistic version [21, 20] for uncertain reasoning. Formal definitions of these frameworks will be given. Many suggestions for semantic operations on values of formulae involving intermediate truth have been made;[41, 40] contain a survey of these. There are two main problems: how to reconcile the use of the linear order [0, 1] as the value space when in reality degrees of truth are often incomparable, and secondly, within this simplified range of values, to select operations which are both logically coherent with each other and intuitively reasonable. We will derive general semantic constraints on operations which will motivate the formal frameworks that we define.
The authors present a real-time programming language, including concurrency, which could be used in the formal development of embedded systems. The semantics of the language is provided in the form of a time interval ...
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We describe the rudiments of algorithm refinement: the business of taking a specification and producing code that correctly implements it. The paper starts with a general discussion of the concepts, and then turns to ...
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We describe the rudiments of algorithm refinement: the business of taking a specification and producing code that correctly implements it. The paper starts with a general discussion of the concepts, and then turns to a particular calculus for algorithm refinement.
Modern functional programming languages and specification formalisms are built around the notion of inductive data types and homomorphisms on these data types. Such homomorphisms, which correspond to the familiar fol...
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Modern functional programming languages and specification formalisms are built around the notion of inductive data types and homomorphisms on these data types. Such homomorphisms, which correspond to the familiar fold or reduce operators in functional programming, are called catamorphisms. It is shown how catamorphisms can be generalized from functions to relations and from relations to predicate transformers. The first step of this generalization, from functions to relations, was achieved in a slightly different setting by Backhouse, de Bruin, Malcolm, Voermans, and van der Woulde (1991). In practical terms, the main result of this analysis is that a calculus based on predicate transformers can be enriched with program constructors for iterating over inductive data types. The refinement calculus did already allow a notion of inductive data types, but until now it lacked the program constructors that are associated with such data types, namely catamorphisms.
The authors present a real-time programming language, including concurrency, which could be used in the formal development of embedded systems. The semantics of the language is provided in the form of a time interval ...
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The authors present a real-time programming language, including concurrency, which could be used in the formal development of embedded systems. The semantics of the language is provided in the form of a time interval semantics and also a number of algebraic refinement laws. The laws allow convenient reasoning and transformation of programs. In particular, a compiler for a sequential subset of the language is defined as a set of theorems relating high-level program constructs to a low-level machine specified as an interpreter in the high-level language. In addition, a prototype compiler may be produced very directly from Ihe lheorems in Ihe form of a logic program.
Formalization presupposes ‘precisification’. A formal representation, therefore, cannot account for all relevant aspects of imprecise domain knowledge. In this paper we present a methodology for dealing with this pr...
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We define non-interference in the algebra of CSP;that definition leads to simple proof rules for non-interference concerning, amongst other things, composition of systems exhibiting non-interference. We work through a...
The author defines non-interference in the algebra of CSP; that definition leads to simple proof rules for non-interference concerning, amongst other things, composition of systems exhibiting non-interference. The aut...
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The author defines non-interference in the algebra of CSP; that definition leads to simple proof rules for non-interference concerning, amongst other things, composition of systems exhibiting non-interference. The author works through a case study of a multi-level secure system to illustrate those laws.< >
This paper describes a design framework for developing application-specific serial array circuits. Starting from a description of the state-transition logic or a fully-parallel architecture, correctness-preserving tra...
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This paper describes a design framework for developing application-specific serial array circuits. Starting from a description of the state-transition logic or a fully-parallel architecture, correctness-preserving transformations are employed to derive a wide range of implementations with different space-time trade-offs. The approach has been used in synthesising designs based on field-programmable gate arrays, and is illustrated by the development of a number of circuits including sorters and convolvers.< >
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