Litak T, Pattinson D, Sano K, Schröder L (2012)
Publication Type: Conference contribution, Original article
Publication year: 2012
Publisher: Springer-verlag
Edited Volumes: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Series: Lecture Notes in Ciomputer Science
City/Town: Berlin
Book Volume: 7392
Pages Range: 299-311
Conference Proceedings Title: Automata, Languages, and Programming
Event location: University of Warwick
ISBN: 9783642315848
URI: http://link.springer.com/chapter/10.1007/978-3-642-31585-5_29
DOI: 10.1007/978-3-642-31585-5_29
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and completeness results for two natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible. We study the expressive power of our language, contrasting it with both coalgebraic modal logic and existing first-order proposals for special classes of Set-coalgebras (apart for relational structures, also neighbourhood frames and topological spaces). The semantic characterization of expressivity is based on the fact that our language inherits a coalgebraic variant of the Van Benthem-Rosen Theorem. Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes which allow for completeness-and in some cases beyond that. © 2012 Springer-Verlag Berlin Heidelberg.
APA:
Litak, T., Pattinson, D., Sano, K., & Schröder, L. (2012). Coalgebraic Predicate Logic. In Automata, Languages, and Programming (pp. 299-311). University of Warwick: Berlin: Springer-verlag.
MLA:
Litak, Tadeusz, et al. "Coalgebraic Predicate Logic." Proceedings of the 39th International Colloquium on Automata, Languages, and Programming , ICALP 2012, University of Warwick Berlin: Springer-verlag, 2012. 299-311.
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