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Generalized Interpolation in CASL
 Information Processing Letter, 76:19–24
, 2000
"... In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not h ..."
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In this paper we consider the partial manysorted firstorder logic and its extension to the subsorted partial manysorted firstorder logic that underly the Casl specification formalism. First we present counterexamples showing that the generalization of the Craig Interpolation Property does not hold for these logics in general (i.e., with respect to arbitrary signature morphisms). Then we formulate conditions under which the generalization of the Craig Interpolation Property holds for the first logic.
A Birkhofflike Axiomatizability Result for Hidden Algebra and Coalgebra
, 2000
"... A characterization result for behaviorally definable classes of hidden algebras shows that a class of hidden algebras is behaviorally definable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically ge ..."
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A characterization result for behaviorally definable classes of hidden algebras shows that a class of hidden algebras is behaviorally definable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a final object and an inclusion system; this is general enough to include all coalgebra categories of interest. As a technical issue, the notions of equation and satisfaction are axiomatized in order to include the different approaches in the literature.
Algebraic treatment of featureoriented systems
 In [12
, 2000
"... Abstract. An important aspect of the feature interaction problem is to formally capture the notion of feature interactions. Although this notion is quite well informally understood by the researchers of the domain, the way, they handle it, strongly depends on the field of investigation they decide t ..."
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Abstract. An important aspect of the feature interaction problem is to formally capture the notion of feature interactions. Although this notion is quite well informally understood by the researchers of the domain, the way, they handle it, strongly depends on the field of investigation they decide to work on (formal method application, architectural conception, technological research...). In this article, we focus on how formally specifying and studying feature systems, and both integration and interaction of features. More precisely, we aim to give a logicindependent framework to deal with the notions of feature, featurebased systems and feature interactions. Then, to help the reader's intuition, we instantiate it by a dynamic algebraic formalism and we give concrete examples of interactions between two features previously described in this formalism.
On Equational Craig Interpolation
, 2000
"... Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications. ..."
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Generalizations of Craig interpolation are investigated for equational logic. Our approach is to do as much as possible at a categorical level, before drawing out the concrete implications.
Correctness of the Logical System for Structured Specifications
 in Algebraic Development Techniques, WADT'97 Seleted Papers. Lecture Notes in Computer Science 1376
, 1997
"... The main aim of this paper is to present the completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its c ..."
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The main aim of this paper is to present the completeness proof of a formal system for reasoning about logical consequences of structured specifications. The system is based on the proof rules for structural specifications build in an arbitrary institution as presented in [ST 88]. The proof of its completeness is inspired by the proof due to M. V. Cengarle (see [Cen 94]) for specifications in firstorder logic and the logical system for reasoning about them presented also in [Wir 91]. 1 Introduction In a number of papers on algebraic specifications (see [Cen 94, Far 92, ST 88, SST 92, Tar 86, Wir 91]) the main goal was to build: ffl a flexible enough specification formalism which allows one to cope with various problems of software engineering; ffl a sound and complete logic for reasoning about such specifications. We follow these goals when the first and a part of the second aim (soundness) is achieved by using structured specifications and the logical system built over an arbitrary...
Behavioral extensions of institutions
, 2005
"... Abstract. We show that any institution I satisfying some reasonable conditions can be transformed into another institution, Ibeh, which captures formally and abstractly the intuitions of adding support for behavioral equivalence and reasoning to an existing, particular algebraic framework. We call ..."
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Abstract. We show that any institution I satisfying some reasonable conditions can be transformed into another institution, Ibeh, which captures formally and abstractly the intuitions of adding support for behavioral equivalence and reasoning to an existing, particular algebraic framework. We call our transformation an “extension ” because Ibeh has the same sentences as I and because its entailment relation includes that of I. Many properties of behavioral equivalence in concrete hidden logics follow as special cases of corresponding institutional results. As expected, the presented constructions and results can be instantiated to other logics satisfying our requirements as well, thus leading to novel behavioral logics, such as partial or infinitary ones, that have the desired properties. 1
A semantic approach to interpolation
 Foundations of Software Science and Computation Structures, 9th International Conference, FOSSACS 2006, volume 3921 of Lecture Notes in Computer Science
, 2006
"... Abstract. Interpolation results are investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify more than twenty interpolation results for firstorder logic and some for richer logics. A few of these results nontrivial ..."
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Abstract. Interpolation results are investigated for various types of formulae. By shifting the focus from syntactic to semantic interpolation, we generate, prove and classify more than twenty interpolation results for firstorder logic and some for richer logics. A few of these results nontrivially generalize known interpolation results. All the others are new. 1
A note on Robinson consistency lemma
, 2006
"... this paper, we propose to make the proof of this result simpler by directly building (i.e. without generating the three chains of elementary morphisms) a model # i with i = 1, 2 such that: 1 ..."
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this paper, we propose to make the proof of this result simpler by directly building (i.e. without generating the three chains of elementary morphisms) a model # i with i = 1, 2 such that: 1
An Incremental Method for the Design of FeatureOriented Systems
"... . Telecommunication systems involve many optional features which cannot be combined according to an obvious definition because they can interact together in an unpredictable way. In order to find the best way to combine features, a major di#culty is to foresee or to discover when a feature can disru ..."
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. Telecommunication systems involve many optional features which cannot be combined according to an obvious definition because they can interact together in an unpredictable way. In order to find the best way to combine features, a major di#culty is to foresee or to discover when a feature can disrupt an another one. Once such an interaction has been analysed, it still remains to define the best combination between the involved features. As this decision is purely subjective, we model the design of featureoriented systems as an iterative process controlled by an expert judgement: all along the process, the expert increases his knowledge about the system under design and thus, may revise the feature integration design w.r.t. his expertise ... until he decides to accept the current feature integration as conform to his ideal view of the system. We propose to jointly adjust the description of a system built by integrating features and the expected properties on the global system all alon...