(Ω, Ξ)-Logic: On the Algebraic Extension of Coalgebraic Specifications

We present an extension of standard coalgebraic specification techniques for state based 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. [9]) 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.