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Interpolation in Grothendieck Institutions
 THEORETICAL COMPUTER SCIENCE
, 2003
"... It is well known that interpolation properties of logics underlying specification formalisms play an important role in the study of structured specifications, they have also many other useful logical consequences. In this paper, we solve the interpolation problem for Grothendieck institutions which ..."
Abstract

Cited by 36 (3 self)
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It is well known that interpolation properties of logics underlying specification formalisms play an important role in the study of structured specifications, they have also many other useful logical consequences. In this paper, we solve the interpolation problem for Grothendieck institutions which have recently emerged as an important mathematical structure underlying heterogenous multilogic specification. Our main result can be used in the applications in several different ways. It can be used to establish interpolation properties for multilogic Grothendieck institutions, but also to lift interpolation properties from unsorted logics to their many sorted variants. The importance of the latter resides in the fact that, unlike other structural properties of logics, many sorted interpolation is a nontrivial generalisation of unsorted interpolation. The concepts, results, and the applications discussed in this paper are illustrated with several examples from conventional logic and algebraic specification theory.
unknown title
, 2003
"... The basic logic programming semantic concepts, query, solutions, solution forms, and the fundamental results such as Herbrand theorems, are developed over any logical system, formalised as institution, by employing ‘institutionindependent’ concepts of variable, substitution, quantifier, and atomic ..."
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The basic logic programming semantic concepts, query, solutions, solution forms, and the fundamental results such as Herbrand theorems, are developed over any logical system, formalised as institution, by employing ‘institutionindependent’ concepts of variable, substitution, quantifier, and atomic formulae. This sets semantical foundations for an uniform development of logic programming over a large variety of computing science logics, allowing for a clean combination of logic programming