Document Type
Article
Publication Date
2004
Abstract
With coalgebras usually being defined in terms of an endofunctor T on sets, this paper shows that modal logics for T-coalgebras can be naturally described as functors L on boolean algebras. Building on this idea, we study soundness, completeness and expressiveness of coalgebraic logics from the perspective of duality theory. That is, given a logic L for coalgebras of an endofunctor T, we construct an endofunctor L such that L-algebras provide a sound and complete (algebraic) semantics of the logic. We show that if L is dual to T, then soundness and completeness of the algebraic semantics immediately yield the corresponding property of the coalgebraic semantics. We conclude by characterising duality between L and T in terms of the axioms of L. This provides a criterion for proving concretely given logics to be sound, complete and expressive.
Recommended Citation
C. Kupke, A. Kurz, and D. Pattinson, “Algebraic Semantics for Coalgebraic Logics,” Electronic Notes in Theoretical Computer Science, vol. 106, pp. 219–241, Dec. 2004. DOI: 10.1016/j.entcs.2004.02.037
Copyright
Elsevier
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Included in
Algebra Commons, Logic and Foundations Commons, Other Computer Engineering Commons, Other Computer Sciences Commons, Other Mathematics Commons
Comments
This article was originally published in Electronic Notes in Theoretical Computer Science, volume 106, in 2004. DOI: 10.1016/j.entcs.2004.02.037