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Interpretability logic
 Mathematical Logic, Proceedings of the 1988 Heyting Conference
, 1990
"... Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbertstyle programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength ..."
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Interpretations are much used in metamathematics. The first application that comes to mind is their use in reductive Hilbertstyle programs. Think of the kind of program proposed by Simpson, Feferman or Nelson (see Simpson[1988], Feferman[1988], Nelson[1986]). Here they serve to compare the strength of theories, or better to prove
A simple proof of arithmetical completeness for ...conservativity logic
, 1996
"... H'ajek and Montagna proved that the modal propositional logic ILM is the logic of \Pi 1 conservativity over sound theories containing I \Sigma 1 (PA with induction restricted to \Sigma 1 formulas). I give a simpler proof of the same fact. ..."
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H'ajek and Montagna proved that the modal propositional logic ILM is the logic of \Pi 1 conservativity over sound theories containing I \Sigma 1 (PA with induction restricted to \Sigma 1 formulas). I give a simpler proof of the same fact.
Modular FirstOrder Ontologies via Repositories
"... From its inception, the focus of ontological engineering has been to support the reusability and shareability of ontologies, as well as interoperability of ontologybased software systems. Among the approaches employed to address these challenges have been ontology repositories and the modularization ..."
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From its inception, the focus of ontological engineering has been to support the reusability and shareability of ontologies, as well as interoperability of ontologybased software systems. Among the approaches employed to address these challenges have been ontology repositories and the modularization of ontologies. In this paper we combine these approaches and use the relationships between firstorder ontologies within a repository (such as nonconservative extension and relative interpretation) to characterize the criteria for modularity. In particular, we introduce the notion of core hierarchies, which are sets of theories with the same nonlogical lexicons and which are all nonconservative extensions of a unique root theory. The technique of relative interpretation leads to the notion of reducibility of a theory to a set of theories in different core hierarchies. We show how these relationships support a semiautomated procedure that decomposes an ontology into irreducible modules. We also propose a semiautomated procedure that can use the relationships between modules to characterize which modules can be shared and reused among different ontologies.