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A semantic approach to interpolation.
 of Lecture Notes in Computer Science,
, 2006
"... Abstract Craig 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 firstorder logic. A few of these results nontrivially generalize known interpolation re ..."
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Abstract Craig 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 firstorder logic. A few of these results nontrivially 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 CraigRobinson version of these results.
LoLa: A Modular Ontology of Logics, Languages, and Translations
 MODULAR ONTOLOGIES, AACHEN. CEUR WORKSHOP PROCEEDINGS
, 2012
"... activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper focuses on the LoLa ontology, which formally describes DOL’s vocabulary for logi ..."
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activity of ISO/TC 37/SC 3, aims at providing a unified framework for (1) ontologies formalised in heterogeneous logics, (2) modular ontologies, (3) links between ontologies, and (4) annotation of ontologies. This paper focuses on the LoLa ontology, which formally describes DOL’s vocabulary for logics, ontology languages (and their serialisations), as well as logic translations. Interestingly, to adequately formalise the logical relationships between these notions, LoLa itself needs to be axiomatised heterogeneously—a task for which we choose DOL. Namely, we use the logic RDF for ABox assertions, OWL for basic axiomatisations of various modules concerning logics, languages, and translations, FOL for capturing certain closure rules that are not expressible in OWL 4, and circumscription for minimising the extension of concepts describing default translations.
Complex software systems : Formalization and Applications *
, 2008
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Horizontal composability revisited
"... We recall the contribution of Goguen and Burstall’s 1980 CAT paper and its powerful influence on theories of specification implementation that were emerging at about the same time, via the introduction of the notions of vertical and horizontal composition of implementations. We then give a differen ..."
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We recall the contribution of Goguen and Burstall’s 1980 CAT paper and its powerful influence on theories of specification implementation that were emerging at about the same time, via the introduction of the notions of vertical and horizontal composition of implementations. We then give a different view of implementation which we believe provides a more adequate reflection of the rather subtle interplay between implementation, specification structure and program structure.
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
Feature Specification: a LogicIndependent Approach
 FUNDAMENTA INFORMATICAE
, 2004
"... In this paper, we investigate the formal specification of features and feature systems in the mathematical paradigm often called "logicindependent", and formally capture in this paradigm the underlying important notions of feature integration and feature interactions. The complexity of ..."
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In this paper, we investigate the formal specification of features and feature systems in the mathematical paradigm often called "logicindependent", and formally capture in this paradigm the underlying important notions of feature integration and feature interactions. The complexity of
On the Algebra of the Structured Specifications
"... We develop module algebra for structured specifications with model oriented denotations. Our work extends the existing theory with specification building operators for nonprotecting importation modes and with new algebraic rules (most notably for initial semantics) and upgrades the pushoutstyle se ..."
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We develop module algebra for structured specifications with model oriented denotations. Our work extends the existing theory with specification building operators for nonprotecting importation modes and with new algebraic rules (most notably for initial semantics) and upgrades the pushoutstyle semantics of parameterized modules to capture the (possible) sharing between the body of the parameterized modules and the instances of the parameters. We specify a set of sufficient abstract conditions, smoothly satisfied in the actual situations, and prove the isomorphism between the parallel and the serial instantiation of multiple parameters. Our module algebra development is done at the level of abstract institutions, which means that our results are very general and directly applicable to a wide variety of specification and programming formalisms that are rigorously based upon some logical system. 1.
A formal denotation of complex systems: how to use algebraic refinement to deal with complexity of systems
, 2008
"... Abstract A mathematical denotation is proposed for the notion of complex software systems whose behavior is specified by rigorous formalisms. Complex systems are described in a recursive way as an interconnection of subsystems by means of architectural connectors. In order to consider the largest ..."
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Abstract A mathematical denotation is proposed for the notion of complex software systems whose behavior is specified by rigorous formalisms. Complex systems are described in a recursive way as an interconnection of subsystems by means of architectural connectors. In order to consider the largest family of specification formalisms and architectural connectors, this denotation is essentially formalism, specification and connectorindependent. For this, we build our denotation on Goguen's institution theory. We then denote in this abstract framework, system complexity by the notion of property emergence and give some conditions to establish when a system is or is not complex. Moreover, we define a refinement theory to deal with the complexity of systems in our generic framework. Indeed, one of the main problem encountered when dealing with complex system is the problem of emergent property detection. In this paper, we propose to use the algebraic refinement technics as a basic incremental method to simplify the emergent property detection. Finally, we illustrate our approach on the formalism classicaly used to specify biological processes: R. Thomas 's genetic regulatory networks (GRNs) over the temporal logic CTL and through the connector of subGRN embedding. 2
Ontohub: A semantic repository for heterogeneous ontologies
 IN: PROC. OF DACS’14 (2014
, 2014
"... Ontohub is a repository engine for managing distributed heterogeneous ontologies. The distributed nature enables communities to share and exchange their contributions easily. The heterogeneous nature makes it possible to integrate ontologies written in various ontology languages. It supports a w ..."
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Ontohub is a repository engine for managing distributed heterogeneous ontologies. The distributed nature enables communities to share and exchange their contributions easily. The heterogeneous nature makes it possible to integrate ontologies written in various ontology languages. It supports a wide range of formal logical and ontology languages building on the OntoIOp.org project and allows for complex intertheory (concept) mappings and relationships with formal semantics. Ontohub aims at satisfying a subset of the requirements for an Open Ontology Repository (OOR). OOR is a longterm international initiative, which has not resulted in a complete implementation so far, but established requirements and designed an architecture. Furthermore, Ontohub is being developed in close connection with the Distributed Ontology Language, which is going to be submitted as response to the Object