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