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An axiomatic approach to structuring specifications

Răzvan Diaconescu
2012 Theoretical Computer Science  
Within this framework we develop concepts and results about 'abstract structured specifications' such as co-limits, model amalgamation, compactness, interpolation, sound and complete proof theory, and  ...  In this paper we develop an axiomatic approach to structured specifications in which both the underlying logical system and corresponding institution of the structured specifications are treated as abstract  ...  Acknowledgment The author thanks the first (anonymous) referee for studying carefully this work and coming up with a series of comments and suggestions that have led to several corrections and an improvement  ... 
doi:10.1016/j.tcs.2012.03.001 fatcat:mxh7nllcbjhvbexessklwfspzy

Modules in Transition - Conservativity, Composition, and Colimits

Oliver Kutz, Till Mossakowski
2007 International Conference on Knowledge Capture  
We outline a general approach for representing combinations of logical theories, or ontologies, through interfaces of various kinds, based on diagrams and the theory of institutions.  ...  Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis?  ...  We thank John Bateman, Joana Hois, and Lutz Schröder for fruitful discussions. Bibliography  ... 
dblp:conf/kcap/KutzM07 fatcat:dq4v6pzcj5coljufposhd54amq

Interpolation in practical formal development

J Bicarregui
2001 Logic Journal of the IGPL  
Interpolation (together with completeness and decidability) has become one of the standard properties that logicians investigate when designing a logic.  ...  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  ...  Uniform interpolants are more appropriate for use in modular specification than ordinary (splitting) interpolants.  ... 
doi:10.1093/jigpal/9.2.231 fatcat:v4tf6vnt6nb47m7qaefu43siny

Modularity results for interpolation, amalgamation and superamalgamation

Silvio Ghilardi, Alessandro Gianola
2018 Annals of Pure and Applied Logic  
It is well-known [21] that for such logics Craig interpolation corresponds to an algebraic property called superamalgamability.  ...  Wolter in [38] proved that the Craig interpolation property transfers to fusion of normal modal logics.  ...  Is it modular also for modal logics on a non-classical basis?  ... 
doi:10.1016/j.apal.2018.04.001 fatcat:3w6ew4vz6zf23a6rf5f6ap576q

A semantic approach to interpolation

Andrei Popescu, Traian Florin Şerbănuţă, Grigore Roşu
2009 Theoretical Computer Science  
By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic.  ...  Interpolation results are investigated for various types of formulae.  ...  For this reason, as well as for reasons coming from theoretical software engineering, in particular from specification theory and modularization [3, 13, 14, 9] , it is quite common today to state interpolation  ... 
doi:10.1016/j.tcs.2008.09.038 fatcat:njalrtgjgbbapjn6xc3umd7qrq

A Semantic Approach to Interpolation [chapter]

Andrei Popescu, Traian Florin Şerbănuţă, Grigore Roşu
2006 Lecture Notes in Computer Science  
By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify a series of interpolation results for first-order logic.  ...  Interpolation results are investigated for various types of formulae.  ...  For this reason, as well as for reasons coming from theoretical software engineering, in particular from specification theory and modularization [3, 13, 14, 9] , it is quite common today to state interpolation  ... 
doi:10.1007/11690634_21 fatcat:mlurqym62vaylaa6fbkx5htenu

Interpolation for predefined types

2011 Mathematical Structures in Computer Science  
For this semantics we develop a generic interpolation result which can be easily applied to various concrete situations from the theory and practice of specification and programming.  ...  We give a logic-independent semantics for predefined (data) types within the categorical abstract model theoretic framework of the theory of institutions.  ...  The generic interpolation result for predefined types is illustrated with a couple of concrete examples involving logics common to specification and logic programming.  ... 
doi:10.1017/s0960129511000430 fatcat:ii2hhaoujza6jigrnib6wbqea4

Conservative extensions, interpretations between theories and all that! [chapter]

T. S. E. Maibaum
1997 Lecture Notes in Computer Science  
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.  ...  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  ...  (Of course, the work on persistence was not directly connected by its inventors with the interpolation and modularity properties.)  ... 
doi:10.1007/bfb0030588 fatcat:rk5h5ieco5gbvkrcwtjzgrwk5m

Page 2570 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
(BR-PCRJ-C; Rio de Janeiro) On pushout consistency, modularity and interpolation for logical specifications. (English summary) Inform. Process. Lett. 60 (1996), no. 2, 59-66.  ...  The paper presents extensions of the three results of the first- order logic known as the modularization theorem, Robinson’s joint consistency theorem and the Craig-Robinson interpolation theorem.  ... 

Abstract Beth definability in institutions

Marius Petria, Răzvan Diaconescu
2006 Journal of Symbolic Logic (JSL)  
One generalises the classical Beth theorem by relying on the interpolation properties of the institution.  ...  Many other applications are expected for the multitude of logical systems formalised as institutions from computing science and logic.  ...  We thank the anonymous referee for checking the submitted version of our paper carefully and competently, which resulted in a correction of a subtle mathematical error and improvement of the presentation  ... 
doi:10.2178/jsl/1154698588 fatcat:4g4hnqvn7vfc7h4bkwxhb6dlcm

Foundations for structuring behavioural specifications

Răzvan Diaconescu, Ionuţ Ţuţu
2014 Journal of Logical and Algebraic Methods in Programming  
We develop foundations for structuring behavioural specifications based on the logic tradition of hidden algebra.  ...  This includes an analysis of a number of important technical compositional properties for behavioural signatures, such as pushouts, inclusions and unions, as well as an investigation of algebraic rules  ...  Acknowledgements We thank both referees for their careful study of our work and for giving us useful feedback, which helped in improving the paper.  ... 
doi:10.1016/j.jlamp.2014.03.001 fatcat:me4znxcbtfgjrbhkkb6j6zsa7m

An Institution-Independent Proof of the Robinson Consistency Theorem

Daniel Gâinâ, Andrei Popescu
2007 Studia Logica: An International Journal for Symbolic Logic  
a signature square in order to satisfy the Robinson consistency and Craig interpolation properties.  ...  This result is then applied to the institution of many-sorted first-order predicate logic and to two of its variations, infinitary and partial, obtaining very general syntactic criteria sufficient for  ...  Rȃzvan Diaconescu also encouraged us and gave us feedback that significantly improved the paper. We also thank Traian Şerbȃnuţȃ, Marius Petria and Cristian Cucu for their insightful suggestions.  ... 
doi:10.1007/s11225-007-9022-4 fatcat:tsavnxfhd5f43e4ndjleqr7i6e

Proof systems for structured algebraic specifications: An overview [chapter]

Rolf Hennicker, Martin Wirsing
1997 Lecture Notes in Computer Science  
proof systems for the underlying logic, may be used for deriving theorems of the specification.  ...  In this paper an overview on proof systems for structured algebraic specifications is presented.  ...  For the completeness the interpolation theorem for infinitary firstorder logic (cf. [Keisler 71]), the normal form theorem (cf.  ... 
doi:10.1007/bfb0036169 fatcat:5zpoo6maefhsbg7gafodmeao2q

The Distributed Ontology, Modeling and Specification Language – DOL [chapter]

Till Mossakowski, Mihai Codescu, Fabian Neuhaus, Oliver Kutz
2015 Studies in Universal Logic  
logics, (3) modular OMS, (4) mappings between OMS, and (5) networks of OMS.  ...  Another diversity appears at the level of ontology, model and specification modularity and relations among ontologies, specifications and models.  ...  We also want to thank Yazmin Angelica Ibañez, Thomas Schneider and Carsten Lutz for valuable input on interpolation and module extraction.  ... 
doi:10.1007/978-3-319-15368-1_21 fatcat:vuhl4ynknzbfhi5s6mxgnw7ihy

Property-oriented semantics of structured specifications

2013 Mathematical Structures in Computer Science  
Institutional preliminaries Following (Goguen and Burstall, 1992) and (Sannella and Tarlecki, 1988) , we abstract away from any particular logical system and study specifications built in an arbitrary  ...  We examine the alternative of sound property-oriented semantics for such specifications, and study their relationship to model-class semantics.  ...  Our thanks to the anonymous reviewers for their perceptive comments, and to one of them for reminding us to explain the relationship to (Goguen and Roşu, 2004) .  ... 
doi:10.1017/s0960129513000212 fatcat:uurpke4xu5d4rdu422kggacca4
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