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Towards heterogeneous specifications. (English) Zbl 0988.03056
Gabbay, Dov M. (ed.) et al., Frontiers of combining systems 2. Selected papers from the 2nd international workshop (FroCoS’98), Amsterdam, Netherlands, October 2-4, 1998. Baldock: Research Studies Press. Stud. Log. Comput. 7, 337-360 (2000).
From the introduction: A necessary prerequisite for sensible use of many logical systems together is that they are linked in some way with each other. In the work on institutions, this is captured by notions of an “arrow” between institutions: institution morphisms (Goguen and Burstall, 1992), maps of institutions (Meseguer, 1989), institution semi-morphisms (Sannella and Tarlecki, 1988), simulations (Astesiano and Cerioli, 1993), representations (Tarlecki, 1987), pre-institution transformations (Salibra and Scollo, 1993). In a previous paper [Lect. Notes Comput. Sci. 1130, 478-502 (1996)], the author gave a systematic presentation of the main concepts and problems in the area together with a possible intuition behind and the possible role for some of these concepts. That paper and some following work by Mossakowski et al. deal mainly with the issues of combining institutions linked by “arrows”, providing rudimentary results for systematic construction of complex logical systems by putting together simpler logics and their extensions.
In the present paper we discuss in some detail what happens with specifications in the presence of a number of institutions linked by arrows of various kinds.
For the entire collection see [Zbl 0978.00029].

03B70 Logic in computer science
68Q65 Abstract data types; algebraic specification
03G30 Categorical logic, topoi
18C10 Theories (e.g., algebraic theories), structure, and semantics