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34
Institution Morphisms
, 2001
"... Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces ..."
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Cited by 65 (18 self)
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Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the "plain maps" of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name "comorphism" over "plain map;" moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider "theoroidal" morphisms and comorphisms, which generalize signatures to theories, based on a theoroidal institution construction, finding that the "maps" of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We introduce "forward" and "seminatural" morphisms, and develop some of their properties. Appendices discuss institutions for partial algebra, a variant of order sorted algebra, two versions of hidden algebra, and...
Heterogeneous specification and the heterogeneous tool set, Habilitation Thesis
, 2005
"... For the specification of large software systems, heterogeneous multilogic specifications are needed, since complex problems have different aspects that are best specified in different logics. True logic combinations (in the sense of fibring [8], or colimits of logical systems [14, 17, 4, 3]) work ..."
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Cited by 32 (19 self)
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For the specification of large software systems, heterogeneous multilogic specifications are needed, since complex problems have different aspects that are best specified in different logics. True logic combinations (in the sense of fibring [8], or colimits of logical systems [14, 17, 4, 3]) work well for certain classes of logics.
Logical Foundations of CafeOBJ
 Theoretical Computer Science
"... This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. T ..."
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Cited by 12 (1 self)
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This paper surveys the logical and mathematical foundations of CafeOBJ, which is a successor of the famous algebraic specification language OBJ but adding several new primitive paradigms such as behavioural concurrent specification and rewriting logic. We first give a concise overview of CafeOBJ. Then we focus on the actual logical foundations of the language at two different levels: basic specification and structured specification, including also the definition of the CafeOBJ institution. We survey some novel or more classical theoretical concepts supporting the logical foundations of CafeOBJ together with pointing to the main results but without giving proofs and without discussing all mathematical details. Novel theoretical concepts include the coherent hidden algebra formalism and its combination with rewriting logic, and Grothendieck (or fibred) institutions. However for proofs and for some of the mathematical details not discussed here we give pointers to relevant publications. ...
The OWL in the CASL Designing Ontologies Across Logics
"... Abstract. In this paper, we show how the web ontology language OWL can be accommodated within the larger framework of the heterogeneous common algebraic specification language HETCASL. Through this change in perspective, OWL can benefit from various useful HETCASL features concerning structuring, mo ..."
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Cited by 6 (1 self)
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Abstract. In this paper, we show how the web ontology language OWL can be accommodated within the larger framework of the heterogeneous common algebraic specification language HETCASL. Through this change in perspective, OWL can benefit from various useful HETCASL features concerning structuring, modularity, and heterogeneity. This tackles a major problem area in ontology engineering: reuse of ontologies and recombination of ontological modules. We discuss in particular: (1) the extension of the Manchester syntax for OWL with structuring mechanisms of CASL, allowing for explicit modularisation; (2) automatic translations between ontology languages to support ontology design across different ontology languages (heterogeneity); (3) heterogeneous ontology refinements, and corresponding automated reasoning support for different logics. 1
Completeness Results for Fibred Parchments Beyond the Propositional Base
 Recent Trends in Algebraic Development Techniques  Selected Papers, volume 2755 of Lecture Notes in Computer Science
, 2003
"... In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of ..."
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Cited by 4 (3 self)
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In [6] it was shown that fibring could be used to combine institutions presented as cparchments, and several completeness preservation results were established. However, their scope of applicability was limited to propositionalbased logics. Herein, we extend these results to a broader class of logics, possibly including variables, terms and quantifiers.
Semantic Web Languages  Towards an Institutional Perspective
, 2006
"... The Semantic Web (SW) is viewed as the next generation of the Web that enables intelligent software agents to process and aggregate data autonomously. Ontology languages provide basic vocabularies to semantically markup data on the SW. We have witnessed an increase of numbers of SW languages in the ..."
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Cited by 4 (0 self)
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The Semantic Web (SW) is viewed as the next generation of the Web that enables intelligent software agents to process and aggregate data autonomously. Ontology languages provide basic vocabularies to semantically markup data on the SW. We have witnessed an increase of numbers of SW languages in the last years. These languages, such as RDF, RDF Schema (RDFS), the OWL suite of languages, the OWL − suite, SWRL, are based on different semantics, such as the RDFSbased, description logicbased, Datalogbased semantics. The relationship among the various semantics poses a challenge for the SW community for making the languages interoperable. Institutions provide a means of reasoning about software specifications regardless of the logical system. This makes it an ideal candidate to represent and reason about the various languages in the Semantic Web. In this paper, we construct institutions for the SW languages and use institution morphisms to relate them. We show that RDF framework together with the RDF serializations of SW languages form an indexed institution. This allows the use of Grothendieck institutions to combine Web ontologies described in various languages.
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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Cited by 3 (0 self)
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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
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
Heterogeneously Structured Ontologies Integration, Connection, and Refinement
"... This paper systematically applies tools and techniques from the area of algebraic specification theory to corresponding ontology structuring and design tasks. We employ the heterogeneous structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining an abstract not ..."
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This paper systematically applies tools and techniques from the area of algebraic specification theory to corresponding ontology structuring and design tasks. We employ the heterogeneous structuring mechanisms of the heterogeneous algebraic specification language HetCasl for defining an abstract notion of structured heterogeneous ontology. This approach enables the designer to split up a heterogeneous ontology into semantically meaningful parts and employ dedicated reasoning tools to them. In particular, we distinguish three fundamentally different kinds of combining heterogeneous ontologies: integration, connection, and refinement.