Journal of Logic, Language and Information

, Volume 17, Issue 1, pp 19–41 | Cite as

A Hybrid Logic for Reasoning about Knowledge and Topology



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.


Topological reasoning The logic of knowledge Hybrid logic Nominalstructure for subset spaces Algebras of sets 


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  1. Blackburn P. (2000) Representation, reasoning, and relational structures: A hybrid logic manifesto. Logic Journal of the IGPL 8: 339–365CrossRefGoogle Scholar
  2. Blackburn P., de Rijke M., Venema Y. (2001) Modal logic Cambridge tracts in theoretical computer science (Vol. 53). Cambridge, Cambridge University Press.Google Scholar
  3. Bourbaki N. (1966) General topology, part 1. Hermann, ParisGoogle Scholar
  4. Dabrowski A., Moss L.S., Parikh R. (1996) Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78: 73–110CrossRefGoogle Scholar
  5. Fagin R., Halpern J.Y., Moses Y., Vardi M.Y. (1995) Reasoning about Knowledge. Cambridge, MA: MIT Press.Google Scholar
  6. 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).Google Scholar
  7. Georgatos K. (1997) Knowledge on treelike spaces. Studia Logica 59: 271–301CrossRefGoogle Scholar
  8. 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.Google Scholar
  9. 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.Google Scholar
  10. Heinemann B. (2004b) The hybrid logic of linear set spaces. Logic Journal of the IGPL 12(3): 181–198CrossRefGoogle Scholar
  11. 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.Google Scholar
  12. 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.Google Scholar
  13. 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. 137–147Google Scholar
  14. 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.Google Scholar
  15. Weiss M.A., Parikh R. (2002) Completeness of certain bimodal logics for subset spaces. Studia Logica 71: 1–30CrossRefGoogle Scholar
  16. 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.Google Scholar

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© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Fakultät für Mathematik und InformatikFernUniversität in HagenHagenGermany

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