Extra Theory Morphisms for Institutions (abstract)
We extend the ordinary concept of theory morphism in
institutions to extra theory morphisms. Extra theory morphisms
map theories belonging to different institutions across institution
morphisms. We investigate the basic mathematical properties of extra
theory morphisms supporting the semantics of logical multi-paradigm
languages, especially module systems a la OBJ-Clear. They include
model reducts, free constructions (liberality), co-limits, and model
amalgamation (exactness).
We outline a general logical semantics for languages whose semantics
satisfy certain ``logical'' principles by extending the institutional semantics
developed within the Clear-OBJ tradition. Finally, in the Appendix, we
briefly illustrate it with the concrete example of CafeOBJ.
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