Abstract
This paper is about a synthesis of two quite different modal reasoning formalisms: the logic of subset spaces, and hybrid logic. Going beyond commonly considered languages we introduce names of objects involving sets and corresponding satisfaction operators, thus increase the expressive power to a large extent. The motivation for our approach is to logically model some general notions from topology like closeness, separation, and linearity, which are of fundamental relevance to spatial or temporal frameworks; in other words, since these notions represent basic properties of space and time we want them to be available to corresponding formal reasoning. We are interested in complete axiomatizations and effectivity properties of the associated logical systems, in particular.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Carlos Areces, Patrick Blackburn, and Maarten Marx. A Road-Map on Complexity for Hybrid Logics. In J. Flum and M. Rodríguez-Artalejo, editors, Computer Science Logic, CSL’99, volume 1683 of Lecture Notes in Computer Science, pages 307–321, Berlin, 1999. Springer.
Patrick Blackburn. Internalizing Labelled Deduction. Journal of Logic and Computation, 10:137–168, 2000.
Patrick Blackburn. Representation, Reasoning, and Relational Structures: a Hybrid Logic Manifesto. Logic Journal of the IGPL, 8:339–365, 2000.
Patrick Blackburn, Maarten de Rijke, and Y de Venema. Modal Logic, volume 53 of Cambridge Track in Theoretical Computer Science. Cambridge University Press, Cambridge, 2001.
Patrick Blackburn and Miroslava Tzakova. Hybrid Languages and Temporal Logic. Logic Journal of the IGPL, 7(1):27–54, 1999.
Nicolas Bourbaki. General Topology, Part 1. Hermann, Paris, 1966.
Andrew Dabrowski, Lawrence S. Moss, and Rohit Parikh. Topological Reasoning and The Logic of Knowledge. Annals of Pure and Applied Logic, 78:73–110, 1996.
Ronald Fagin, Joseph Y. Halpern, Yoram Moses, and Moshe Y. Vardi. Reasoning about Knowledge. MIT Press, Cambridge, MA, 1995.
Konstantinos Georgatos. Knowledge on Treelike Spaces. Studia Logica, 59:271–301, 1997.
Bernhard Heinemann. About the Temporal Decrease of Sets. In C. Bettini and A. Montanari, editors, Temporal Representation and Reasoning, 8th International Workshop, TIME-01, pages 234–239, Los Alamitos, CA, 2001. IEEE Computer Society Press.
Bernhard Heinemann. Hybrid Languages for Subset Spaces. Informatik Berichte 290, FernUniversität, Hagen, October 2001.
Bernhard Heinemann. Linear Tense Logics of Increasing Sets. Journal of Logic and Computation, 12, 2002. To appear.
Maarten Marx and Y de Venema. Multi-Dimensional Modal Logic, volume 4 of Applied Logic Series. Kluwer Academic Publishers, Dordrecht, 1997.
Klaus Weihrauch. Computable Analysis. Springer, Berlin, 2000.
M. Angela Weiss. Completeness of Certain Bimodal Logics for Subset Spaces. Ph.D. thesis, The City University of New York, New York, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Heinemann, B. (2002). A Hybrid Treatment of Evolutionary Sets. In: Coello Coello, C.A., de Albornoz, A., Sucar, L.E., Battistutti, O.C. (eds) MICAI 2002: Advances in Artificial Intelligence. MICAI 2002. Lecture Notes in Computer Science(), vol 2313. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46016-0_22
Download citation
DOI: https://doi.org/10.1007/3-540-46016-0_22
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43475-7
Online ISBN: 978-3-540-46016-9
eBook Packages: Springer Book Archive