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Formal Interoperability
, 1998
"... this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss: ..."
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Cited by 13 (3 self)
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this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss:
Notes on Refinement, Interpolation and Uniformity.
"... The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of th ..."
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Cited by 6 (5 self)
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The connection between some modularity properties and interpolation is revisited and restated in a general "logicindependent " framework. The presence of uniform interpolants is shown to assist in certain proof obligations, which suffice to establish the composition of refinements. The absence of the desirable interpolation properties from many logics that have been used in refinement, motivates a thorough investigation of methods to expand a specification formalism orthogonally, so that the critical uniform interpolants become available. A potential breakthrough is outlined in this paper. 1. A refinement paradigm Let us consider program development by means of stepwise refinements. One postulates some abstract data typelike specification 1 (ADT), suitable for the problem at hand, which has to be implemented on the available system. The end product consists of (the text of) an abstract program manipulating the postulated ADT, together with a suite of (texts of) modules implementin...
Integrating Heterogeneous Formalisms: Framework and Application
, 1999
"... In this paper we study the problem of integrating heterogeneous formal notations, emphasising the integration of the axiomatic (logical) semantics. We present a general method for integrating the consequence systems of interrelated heterogeneous formal notations and explain why and when the resultin ..."
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Cited by 1 (1 self)
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In this paper we study the problem of integrating heterogeneous formal notations, emphasising the integration of the axiomatic (logical) semantics. We present a general method for integrating the consequence systems of interrelated heterogeneous formal notations and explain why and when the resulting compound muiltilogical consequence system may need the additional support of structural ("locality") axioms in order to incorporate the interrelations between the components. We illustrate the use of this method as a basis for the integration of VDM and B formalisms based on LPF and Classical logic.
Modularity and Interpolation in a Development Workspace.
, 1997
"... The potential benefits of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easytoderive, uniform presentation of the interpolants is supported. This paper p ..."
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Cited by 1 (1 self)
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The potential benefits of a uniform version of interpolation are hindered by its absence from many expressive logics. This motivates a thorough investigation of appropriate expansions of known entailments so that an easytoderive, uniform presentation of the interpolants is supported. This paper presents the skeleton of a general construction and indicates that a potentially large class of entailments can be extended so that a uniform presentation of the interpolants is available. 1 Introduction There is a well established relation between interpolation [8] and modularity properties of refinements [23, 24, 29, 5, 32, 40, 39, 12, 11] and databases [25]. On the other hand, many logics that have been used in refinement or databases lack the desirable interpolation properties. To compensate for this inadequacy, several groups of researchers have proposed techniques to restrict these logics to fragments that have the desirable modularity properties. Some of these enterprises have focuse...
Uniformity, Interpolation and Module specification in a Development Workspace
 the proceedings of the TFM'98 workshop
, 1997
"... . Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating specification modules. In addition, the presence of a Uniform presentation of interpolants facilitates the specification of modules. Also, the a ..."
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Cited by 1 (1 self)
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. Interpolation and Schematic Reasoning are shown to underlie critical and somewhat complementary aspects of designing and (syntactically) manipulating specification modules. In addition, the presence of a Uniform presentation of interpolants facilitates the specification of modules. Also, the ability to encapsulate and manipulate Uniform Schemata may assist us in reasoning with (abstractions of) hidden data. Unfortunately, most formalisms that have been used in fundamental approaches to software engineering lack uniform interpolation and do not directly support schematic reasoning. This paper reveals the critical role of uniform interpolants and uniform schemata from the perspective of modularity, and quotes a general construction indicating that a potentially large class of calculi can be extended conservatively so that a uniform presentation of the critical interpolants becomes available and the manipulation of uniform schemata is supported. 1 Introduction There is a ...
On a Generalised Modularisation Theorem
, 2000
"... The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order logic (the ..."
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Cited by 1 (0 self)
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The relation between a metalogical property of entailment (interpolation) and a structural property of categories of theory presentations (stability of faithful morphisms under pushouts) is studied in an abstract "general logic" framework. In particular, a known result for first order logic (the "modularisation theorem"), stating that the stability of faithful morphisms under pushouts is equivalent to a specific form of interpolation, is generalised and reestablished. Furthermore, the stability under pushouts of the faithfulness of a given theory interpretation is shown to be equivalent to the existence of interpolants on specific loci of the underlying formalism. The latter neither assumes nor requires that the underlying logic possesses interpolation globally. 1 Introduction In this paper we revise, generalise and reestablish, in a notation independent framework, a strong relation between (a form of) interpolation [5, 20, 29, 1] and the stability of conservative extensio...
Development Workspaces: an introduction
"... Interpolation and schematic reasoning underlie critical and somewhat complementary aspects of the design and manipulation of specification modules. Unfortunately, many formalisms that have been used in formal approaches to software engineering lack uniform interpolation and do not directly suppor ..."
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Interpolation and schematic reasoning underlie critical and somewhat complementary aspects of the design and manipulation of specification modules. Unfortunately, many formalisms that have been used in formal approaches to software engineering lack uniform interpolation and do not directly support schematic reasoning. This paper presents the skeleton of a novel general construction for extending conservatively a base entailment system Espec to an entailment system Edev such that Edev provides a uniform presentation of interpolants for entailments between Especsentences and supports the precise logical encapsulation of uniform schemata on Espec . This conservative extension is presented by means of a Subentailment system hEspec ; J : Espec!Edevi called a Development Workspace on Espec . 1 Introduction There is a well established relation between interpolation [6, 21, 31, 2] and modularity properties of refinement via implementations (eg., [12, 11, 10] and [22, 23, 41, 38, 4...