H.-J. Kreowski and T. Mossakowski. Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras. Math. Struct. in Comp. Sci., 5:189--215, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....they contain embeddings as a subcategory. I am indebted to Till Mossakowski for pointing out that the above notion of extension map is closely related to his notion of categorical retractive simulation, which is a map of institutions ( Phi; ff; fi) with a right inverse left adjoint for each fi T [19]. In fact, categorical retractive simulations are a special case of the more general notion of an extension map. The following proposition shows that if an institution I 0 has an entailment system making it into a complete logic, then we can use an extension map I ae I 0 to borrow such an ....

H.-J. Kreowski and T. Mossakowski. Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras. Math. Struct. in Comp. Sci., 5:189--215, 1995.

.... introduced simple institution maps [43] which generalize comorphisms by mapping signatures to theories; some variations, including conjunctive maps which take a sentence to a set of sentences, were studied by Mossakowski [45] who with Kreowski also introduced embeddings of institutions [38], to formalize equivalence of logical frameworks; Sannella and Tarlecki introduced semi morphisms [61, 67] which only have models, for relating specification and implementation languages, and Salibra and Scollo introduced transformations [57] which map models to sets of models. Diaconescu ....

Hans-Jorg Kreowski and Till Mossakowski. Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras. Mathematical Structures in Computer Science, 5(2):189--215, June 1995.

....[15] Notice that the terminology institution embedding is used also by Meseguer [29] but in a completely different sense. Also, several variants of persistent institution morphism have been independently introduced in the literature, such that the categorical retractive simulations of [26] and the extension maps of [29] 3 Extra Theory Morphisms Extra theory morphisms generalize the ordinary concept of theory morphism (Definition 2) in that they map theories across an institution morphism. Intra (i.e. ordinary) theory morphisms can be regarded as special cases when the ....

H.-J. Kreowski and Till Mossakovski. Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras. Mathematical Strcutures in Computer Science, 5:189--215, 1995.

.... institution embedding is used also by (Meseguer, 1998) but in a completely different sense. Besides (Diaconescu, 1998) several stronger variants of liberal institution homomorphisms have been independently introduced in the literature, such that the categorical retractive simulations of (Kreowski and Mossakovski, 1995) and the extension maps of (Meseguer, 1998) Exact institution embeddings are a novel concept which expresses the primitive possibility of amalgamation of consistent models across an institution embedding. 3. Grothendieck Institutions The following definition generalises the concept of indexed ....

Kreowski, H.-J. and T. Mossakovski: 1995, `Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras'. Mathematical Structures in Computer Science 5, 189--215.

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