Topological systems as a framework for institutions. (English) Zbl 1394.18002
Summary: Recently, J. T. Denniston et al. [Fuzzy Sets Syst. 192, 58–103 (2012; Zbl 1244.54013)] introduced a lattice-valued analogue of the concept of institution of J. A. Goguen and R. M. Burstall [Lect. Notes Comput. Sci. 164, 221–256 (1984; Zbl 0543.68021)], comparing it, moreover, with the (lattice-valued version of the) notion of topological system of S. Vickers [Topology via logic. Cambridge etc.: Cambridge University Press (1989; Zbl 0668.54001)]. In this paper, we show that a suitable generalization of topological systems provides a convenient framework for certain kinds of (lattice-valued) institutions.
MSC:
| 18B30 | Categories of topological spaces and continuous mappings (MSC2010) |
| 54B30 | Categorical methods in general topology |
| 68Q65 | Abstract data types; algebraic specification |
Keywords:
adjoint situation; affine theory; comma category; elementary institution; localification and spatialization procedure; topological institution; topological space; topological system; variety of algebrasReferences:
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