We present an extension of standard coalgebraic specification techniques for statebased systems which allows us to integrate constants and n-ary operations in a smooth way and, moreover, leads to a simplification of the coalgebraic structure of the models of a specification. The framework of (Ω,Ξ)-logic can be considered as the result of a translation of concepts of observational logic (cf. ) into the coalgebraic world. As a particular outcome we obtain the notion of an (Ω, Ξ)- structure and a sound and complete proof system for (first-order) observational properties of specifications.
R. Hennicker and A. Kurz, “(Ω, Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications,” Electronic Notes in Theoretical Computer Science, vol. 19, pp. 164–180, 1999. DOI: 10.1016/S1571-0661(05)80275-0
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