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Logical Support for Modularisation
 LOGICAL ENVIRONMENTS
, 1993
"... Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of ..."
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Cited by 97 (31 self)
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Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of modules. Our results show some new connections among: (1) the preservation of various kinds of conservative extension under pushouts; (2) various distributive laws for information hiding over sums; and (3) (Craig style) interpolation properties. In addition, we study differences between syntactic and semantic formulations of conservative extension properties, and of distributive laws. A model theoretic property that we call exactness plays an important role in some results. This paper explores the interplay between syntax and semantics, and thus lies in the tradition of abstract model theory. We represent logical systems as institutions. An important technical foundation is a new ...
Logicbased ontology comparison and module extraction, with an application to DLLite
 ARTIFICIAL INTELLIGENCE
, 2010
"... We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between on ..."
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Cited by 24 (8 self)
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We develop a formal framework for comparing different versions of DLLite ontologies. The main feature of our approach is that we take into account the vocabulary ( = signature) with respect to which one wants to compare ontologies. Five variants of difference and inseparability relations between ontologies are introduced and their respective applications for ontology development and maintenance discussed. These variants are obtained by generalising the notion of conservative extension from mathematical logic and by distinguishing between differences that can be observed among concept inclusions, answers to queries over ABoxes, by taking into account additional context ontologies, and by considering a modeltheoretic, languageindependent notion of difference. We compare these variants, study their metaproperties, determine the computational complexity of the corresponding reasoning tasks, and present decision algorithms. Moreover, we show that checking inseparability can be automated by means of encoding into QBF satisfiability and using offtheshelf general purpose QBF solvers. Inseparability relations between ontologies are then used to develop a formal framework for (minimal) module extraction. We demonstrate that different types of minimal modules induced by these inseparability relations can be automatically extracted from realworld mediumsize DLLite ontologies by composing the tractable syntactic localitybased module extraction algorithm with nontractable extraction algorithms using the multiengine QBF solver aqme. Finally, we explore the relationship between uniform interpolation (or forgetting) and inseparability between ontologies.
Formal Properties of Modularisation
"... Summary. Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these pro ..."
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Cited by 14 (5 self)
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Summary. Modularity of ontologies is currently an active research field, and many different notions of a module have been proposed. In this paper, we review the fundamental principles of modularity and identify formal properties that a robust notion of modularity should satisfy. We explore these properties in detail in the contexts of description logic and classical predicate logic and put them into the perspective of wellknown concepts from logic and modular software specification such as interpolation, forgetting and uniform interpolation. We also discuss reasoning problems related to modularity. 1
A General Method for Safely Overwriting Theories in Mechanized Mathematics Systems
 Lecture Notes in Computer Science (Proc. Intl. Zurich Sem. Digital Comm.). Spinger
, 1994
"... We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as we ..."
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Cited by 2 (1 self)
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We propose a general method for overwriting theories with model conservative extensions in mechanized mathematics systems. Model conservative extensions, which include the denition of new constants and the introduction of new abstract datatypes, are \safe" because they preserve models as well as consistency. The method employs the notions of theory interpretation and theory instantiation. It is illustrated using manysorted rstorder logic, but it works for a variety of underlying logics. Supported by the MITRESponsored Research program. 1 1 Introduction Mathematical reasoning is always performed in some mathematical context consisting of vocabulary and assumptions. The formal counterpart of a context is a theory consisting of a formal language plus a set of sentences of the language called axioms. (We will denote a theory T by the pair (L; ) where L is the formal language of T and is the set of axioms of T .) An extension of a theory T is any theory T 0 obtained by ...
ModelTheoretic Inseparability and Modularity of Description Logic Ontologies
"... The aim of this paper is to introduce and study modeltheoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called modeltheoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ ..."
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The aim of this paper is to introduce and study modeltheoretic notions of modularity in description logic and related reasoning problems. Our approach is based on a generalisation of logical equivalence that is called modeltheoretic inseparability. Two TBoxes are inseparable w.r.t. a vocabulary Σ if they cannot be distinguished by the Σreducts of their models and thus can equivalently be replaced by one another in any application where only vocabulary items from Σ are relevant. We study indepth the complexity of deciding inseparability for the description logics EL and ALC and their extensions with inverse roles. We then discuss notions of modules of a TBox based on modeltheoretic inseparability and develop algorithms for extracting minimal modules from acyclic TBoxes. Finally, we provide an experimental evaluation of our module extraction algorithm based on the largescale medical TBox Snomed ct. 1.