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Borrowing Interpolation
, 2011
"... We present a generic method for establishing interpolation properties by ‘borrowing ’ across logical systems. The framework used is that of the so-caled ‘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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Cited by 4 (1 self)
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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 so-caled ‘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.
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"... Abstract. This chapter surveys approaches to handling categorical systems of extensive size, spanning from semi-formal systems in terminology and classification sciences to formal logical approaches. In particular, we briefly review the transition from terminologies to ontologies that are formalize ..."
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Abstract. This chapter surveys approaches to handling categorical systems of extensive size, spanning from semi-formal systems in terminology and classification sciences to formal logical approaches. In particular, we briefly review the transition from terminologies to ontologies that are formalized in logics, exemplified in the medical domain. The main part presents the state of the art of the modularization of logical theories with an ontology-related background. Since the field is still very young and active, an evaluation of these approaches results in a heterogeneous landscape of proposals and leaves perspectives for future research.
Interpolation for Predefined Types
- UNDER CONSIDERATION FOR PUBLICATION IN MATH. STRUCT. IN COMP. SCIENCE
, 2008
"... ... model theoretic framework of the theory of institutions. For this semantics we develop a generic interpolation result which can be easily applied to various concrete situations from the theory and practice of specification and programming. Our study of interpolation is motivated by a number of i ..."
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... model theoretic framework of the theory of institutions. For this semantics we develop a generic interpolation result which can be easily applied to various concrete situations from the theory and practice of specification and programming. Our study of interpolation is motivated by a number of important applications to computing science especially in the area of structured specifications.
Towards a Functional Approach to Modular Ontologies using Institutions
"... We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query lang ..."
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We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.
Towards a Functional Approach to Modular Ontologies using Institutions
"... Abstract. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a ..."
Abstract
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Abstract. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We then generalise existing notions of robustness from the literature, and relate these to interpolation properties that support modularisation of ontologies.
