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Interpolation in Practical Formal Development
 LOGIC JOURNAL OF THE IGPL
, 2001
"... 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 prac ..."
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Cited by 9 (2 self)
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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.
The distributed ontology, modeling and specification language  DOL
, 2013
"... There is a diversity of ontology languages in use, among them OWL, RDF, OBO, Common Logic, and Flogic. Related languages such as UML class diagrams, entityrelationship diagrams and object role modelling provide bridges from ontology modelling to applications, e.g. in software engineering and datab ..."
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Cited by 9 (6 self)
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There is a diversity of ontology languages in use, among them OWL, RDF, OBO, Common Logic, and Flogic. Related languages such as UML class diagrams, entityrelationship diagrams and object role modelling provide bridges from ontology modelling to applications, e.g. in software engineering and databases. Another diversity appears at the level of ontology modularity and relations among ontologies. There is ontology matching and alignment, module extraction, interpolation, ontologies linked by bridges, interpretation and refinement, and combination of ontologies. The Distributed Ontology, Modelling and Specification Language (DOL) aims at providing a unified meta language for handling this diversity. In particular, DOL provides constructs for (1) “asis ” use of ontologies formulated in a specific ontology language, (2) ontologies formalised in heterogeneous logics, (3) modular ontologies, and (4) links between ontologies. This paper sketches the design of the DOL language. DOL will be submitted as a proposal within the OntoIOp (Ontology Integration and Interoperability) standardisation activity of the Object Management Group (OMG).
Hybridization of Institutions
"... Abstract. Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for nami ..."
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Abstract. Modal logics are successfully used as specification logics for reactive systems. However, they are not expressive enough to refer to individual states and reason about the local behaviour of such systems. This limitation is overcome in hybrid logics which introduce special symbols for naming states in models. Actually, hybrid logics have recently regained interest, resulting in a number of new results and techniques as well as applications to software specification. In this context, the first contribution of this paper is an attempt to ‘universalize ’ the hybridization idea. Following the lines of [16], where a method to modalize arbitrary institutions is presented, the paper introduces a method to hybridize logics at the same institutionindependent level. The method extends arbitrary institutions with Kripke semantics (for multimodalities with arbitrary arities) and hybrid features. This paves the ground for a general result: any encoding (expressed as comorphism) from an arbitrary institution to first order logic (FOL) determines a comorphism from its hybridization to FOL. This second contribution opens the possibility of effective tool support to specification languages based upon logics with hybrid features. 1
Abstract specification theory: an overview
 Logics of Engineering Software
, 2003
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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.
Modules in transition. Conservativity, Composition, and Colimits
 In Proceedings, Second International Workshop on Modular Ontologies
, 2007
"... Abstract. Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis? We propose to use the language of category theory, in particular diagrams and their colimits, for answering this question. We outline a general approach for representing c ..."
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Abstract. Several modularity concepts for ontologies have been studied in the literature. Can they be brought to a common basis? We propose to use the language of category theory, in particular diagrams and their colimits, for answering this question. 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. In particular, we consider theory interpretations, language extensions, symbol identification, and conservative extensions. We study the problem of inheriting conservativity between subtheories in a diagram to its colimit ontology. Finally, we apply this to the problem of conservativity when composing DDLs or Econnections. 1
Three decades of institution theory.
 In JeanYves Beziau, editor, Universal Logic: an Anthology,
, 2012
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Structured CSP  A Process Algebra as an Institution
, 2007
"... We introduce two institutions for the process algebra Csp, one for the traces model, and one for the stable failures model. The construction is generic and should be easily instantiated with further models. As a consequence, we can use structured specification constructs like renaming, hiding and p ..."
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We introduce two institutions for the process algebra Csp, one for the traces model, and one for the stable failures model. The construction is generic and should be easily instantiated with further models. As a consequence, we can use structured specification constructs like renaming, hiding and parameterisation (that have been introduced over an arbitrary institution) also for Csp. With a small example we demonstrate that structuring indeed makes sense for Csp.
An Axiomatic Approach to Structuring Specifications
"... 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 institutions, which means two levels of institution independence. This abstract axiomatic app ..."
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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 institutions, which means two levels of institution independence. This abstract axiomatic approach provides a uniform framework for the study of structured specifications independently from any actual choice of specification building operators, and moreover it unifies the theory and the model oriented approaches. Within this framework we develop concepts and results about ‘abstract structured specifications ’ such as colimits, model amalgamation, compactness, interpolation, sound and complete proof theory, and pushoutstyle parameterization with sharing, all of them in a top down manner dictated by the upper level of institution independence. 1.
Borrowing Interpolation
, 2011
"... We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the socaled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a ..."
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We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the socaled ‘institution theory’ which is a categorical abstract model theory providing a formal definition for the informal concept of ‘logical system’ and a mathematical concept of ‘homomorphism’ between logical systems. We develop three different styles or patterns to apply the proposed borrowing interpolation method. These three ways are illustrated by the development of a series of concrete interpolation results for logical systems that are used in mathematical logic or in computing science, most of these interpolation properties apparently being new results. These logical systems include fragments of (classical many sorted) first order logic with equality, preordered algebra and its Horn fragment, partial algebra, higher order logic. Applications are also expected for many other logical systems, including membership algebra, various types of order sorted algebra, the logic of predefined types, etc., and various combinations of the logical systems discussed here.