Abstract
We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Blackburn P. (2000) Representation, reasoning, and relational structures: A hybrid logic manifesto. Logic Journal of the IGPL 8: 339–365
Blackburn P., de Rijke M., Venema Y. (2001) Modal logic Cambridge tracts in theoretical computer science (Vol. 53). Cambridge, Cambridge University Press.
Bourbaki N. (1966) General topology, part 1. Hermann, Paris
Dabrowski A., Moss L.S., Parikh R. (1996) Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78: 73–110
Fagin R., Halpern J.Y., Moses Y., Vardi M.Y. (1995) Reasoning about Knowledge. Cambridge, MA: MIT Press.
Georgatos, K. (1994). Knowledge theoretic properties of topological spaces. In M. Masuch & L. Pólos (Eds.), Knowledge representation and uncertainty, logic at work Lecture notes in artificial intelligence (Vol. 808, pp. 147–159).
Georgatos K. (1997) Knowledge on treelike spaces. Studia Logica 59: 271–301
Heinemann, B. (2003). Extended canonicity of certain topological properties of set spaces. In M. Vardi & A. Voronkov (Eds.), Logic for programming, artificial intelligence, and reasoning, Lecture notes in artificial intelligence. (Vol. 2850, pp. 135–149). Berlin: Springer.
Heinemann, B. (2004a). A hybrid logic of knowledge supporting topological reasoning. In C. Rattray, S. Maharaj, & C. Shankland (Eds.), Algebraic methodology and software technology, AMAST 2004, Lecture notes in computer science. (Vol. 3116, pp. 181–195). Berlin: Springer.
Heinemann B. (2004b) The hybrid logic of linear set spaces. Logic Journal of the IGPL 12(3): 181–198
Heinemann, B. (2005a). Algebras as knowledge structures. In J. Jedrzejowicz & A. Szepietowski (Eds.), Mathematical foundations of computer science, MFCS 2005, Lecture notes in computer science (Vol. 3618, pp. 471–482). Berlin: Springer.
Heinemann, B. (2005b). A spatio-temporal view of knowledge. In I. Russell & Z. Markov (Eds.), Proceedings 18th International Florida Artificial Intelligence Research Society Conference (FLAIRS 2005) (pp. 703–708). Menlo Park, CA.
Krommes G. (2003) A new proof of decidability for the modal logic of subset spaces. In: ten Cate B. (eds) Proceedings of the Eighths ESSLLI Student Session. Vienna, Austria, pp. 137–147
Moss, L. S., & Parikh, R. (1992). Topological reasoning and the logic of knowledge. In Y. Moses (Ed.), Theoretical aspects of reasoning about knowledge (TARK 1992) (pp. 95–105). San Francisco, CA: Morgan Kaufmann.
Weiss M.A., Parikh R. (2002) Completeness of certain bimodal logics for subset spaces. Studia Logica 71: 1–30
Wu, Y., & Weihrauch, K. (2005). A computable version of the daniell–stone theorem on integration and linear functionals. In V. Brattka, L. Staiger, & K. Weihrauch (Eds.), Proceedings of the 6th Workshop on Computability and Complexity in Analysis, Electronic notes in theoretical computer science (Vol. 120, pp. 95–105). Amsterdam.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Heinemann, B. A Hybrid Logic for Reasoning about Knowledge and Topology. J of Log Lang and Inf 17, 19–41 (2008). https://doi.org/10.1007/s10849-007-9043-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-007-9043-4