Axiomatising Specification Theory

Maibaum, Tom; Sadler, M. R.

doi:10.1007/978-3-662-09691-8_13

Cited by 14 publications

(9 citation statements)

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“…Second, an equivalence between a generalisation of a "splitting" variant of interpolation and a generalisation of the so called "modularization" property (ie., stability of theorem conservation under amalgmation) has been established in [20] for every (structured) family of reflexive, transitive and monotonic entailment relations. Such an equivalence was earlier conjectured in [35] (see also [32] and [33]). Detailed proofs for unsorted first order logic were given in [47] and in [48].…”

Section: Interpolation In Specification Theorysupporting

confidence: 76%

Interpolation in practical formal development

Bicarregui

Dimitrakos²,

Gabbay

et al. 2001

Logic Journal of IGPL

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Interpolation (together with completeness and decidability) has become one of the standard properties that logicians investigate when designing a logic. In this paper, we provide strong evidence that the presence of interpolants is not only cogent for scientific reasoning but has also important practical implications in computer science. We illustrate that interpolation in general, and uniform splitting interpolants, in particular, play an important role in applications where formality and modularity are invoked. In recognition of the fact that common logical formalisms often lack uniform interpolants, we advocate the need for developing general methods to (re)engineer a specification logic so that (at least) some critical uniform interpolants become available.

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Section: Interpolation In Specification Theorysupporting

confidence: 76%

Interpolation in practical formal development

Bicarregui

Dimitrakos²,

Gabbay

et al. 2001

Logic Journal of IGPL

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“…A related stronger property is Craig-Robinson interpolation (CRI). Some researchers [24,16] have argued that CRI, and not just CI, is desirable in algebraic specification frameworks. First-order logic has CRI, and so does any logic which has CI, is compact and has implications [12].…”

Section: Craig-robinson Interpolationmentioning

confidence: 98%

A semantic approach to interpolation

Popescu

erbnu

Rou

2009

Theoretical Computer Science

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a b s t r a c tCraig interpolation is investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic. A few of these results non-trivially generalize known interpolation results; all the others are new. We also discuss some applications of our results to the theory of institutions and of algebraic specifications, and a Craig-Robinson version of these results.Published by Elsevier B.V.

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“…Notes: Conservative extensions are essential for explaining parameterisation [38,39,40,41,50] (as the 'body' of the parameterised specification is a conservative extension of the specification of the formal parameter) and the concept of implementation.…”

Section: Technical Assumptions and Toolsmentioning

confidence: 99%

“…In retrospect, this is straightforward, but it was a bit of surprise to us category-phobes! The observation having been made, there was an obvious route to generalisation (first mooted in [38]), in terms of n-institutions ( [18]). These latter are a proof theoretic generalisation of institutions, with consequence replacing satisfaction as the focus of attention 4.…”

Section: The Appearance Of a Universal Lawmentioning

confidence: 99%

Conservative extensions, interpretations between theories and all that!

Maibaum

1997

TAPSOFT '97: Theory and Practice of Software Development

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Abstract. About twenty years ago, together with a group of collaborators, some conjectures were developed about the fundamental principles of a theory of specification. These principles included the use of interpretations between theories to underpin the concept of representation and parameterisation, conservative extensions to underpin the concept of modularity and extraiogieal equality to deal with multiple representations. It was quickly realised that there were fundamental metalogical properties which amounted to 'laws' of specification. An example is provided by the role of Craig interpolation in the composability of implementations and parameter instantiation. Further work on institutions added some fundamental ideas about generalising some of these concepts to logics other than many sorted first order Iogie and pointed out the eategorieal nature of many of the constructions. Recent work has highlighted the possibility of 'intemalising' some of the meta concepts involved and led to a re-examination of the fundamental principles. For example, extralogieal equality and general interpretations are not as fundamental as we thoughttwenty years ago. The purpose of the paper is to present a retrospective on this work and outline the basic principles of a general theory of specification as we now see it.

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Axiomatising Specification Theory

Cited by 14 publications

References 1 publication

Interpolation in practical formal development

Interpolation in practical formal development

A semantic approach to interpolation

Conservative extensions, interpretations between theories and all that!

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