\((\Omega,\Xi)\)-logic: On the algebraic extension of coalgebraic specifications. (English) Zbl 0918.68064

Hennicker, Rolf; Kurz, Alexander

Jacobs, Bart (ed.) et al., CMCS ‘99. Proceedings of the 2nd workshop on Coalgebraic methods in computer science. A satellite event to the European joint conferences on Theory and practice of software, ETAPS ‘99. Amsterdam, the Netherlands, March 20–21, 1999. Amsterdam: Elsevier, Electronic Notes in Theoretical Computer Science. 19, electronic paper No. 12 (1999).

Summary: 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 \((\Omega,\Xi)\)-logic can be considered as the result of a translation of concepts of observational logic into the coalgebraic world. As a particular outcome we obtain the notion of an \((\Omega,\Xi)\)-structure and a sound and complete proof system for (first-order) observational properties of specifications.
For the entire collection see [Zbl 0916.00017].

MSC:

68Q65

Abstract data types; algebraic specification

Keywords:

coalgebraic specification techniques