Document Type
Article
Publication Date
2008
Abstract
Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate to any set-functor T a complete (finitary) logic L consisting of modal operators and Boolean connectives.
Recommended Citation
A. Kurz and D. Petrişan, “Functorial Coalgebraic Logic: The Case of Many-sorted Varieties,” Electronic Notes in Theoretical Computer Science, vol. 203, no. 5, pp. 175–194, Jun. 2008. DOI: 10.1016/j.entcs.2008.05.025
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 203, issue 5, in 2008. DOI: 10.1016/j.entcs.2008.05.025