Vol. 31 No. 1 (2011)
Articles

Hacia una lógica temporal-epistémica basada en lenguajes híbridos

José Rafael Herrera González
Universidad de La Laguna / Grupo LEMA
Margarita Vázquez Campos
Universidad de La Laguna / Grupo LEMA

Published 2011-05-01

Keywords

  • Lógica epistémica,
  • Lógica temporal,
  • Lógica híbrida,
  • Combinación de lógicas
  • Epistemic Logic,
  • Temporal logic,
  • Hybrid logic,
  • Combining logics

Abstract

Our main goal in this paper is to analyse if it is possible to build some suitable Temporal-Epistemic Systems. However, the main difficulties in order to aim this goal come from the fact of having to combine an absolute temporal perspective with a relative (to each agent) epistemic perspective; that is, on one hand, temporal points (instants) are determined from the point of view of an observer placed outside the world, and, on the other hand, the epistemic alternatives of each agent (in each instant) are relative to that agent. We think that some of these difficulties could be solved with the help of hybrid logics, because this kind of logics simplifies the combination of temporal and epistemic systems, and so we can avoid building highly complicated models.

References

  1. Areces, C., Blackburn, P. y Marx, M. (2001), “Hybrid Logics: Characterization, Interpolation and Complexity”, The Journal of Symbolic Logic, 6 (3), pp. 977-1009.
  2. Blackburn, P. (1994), “Tense, Temporal Reference and Tense Logic”, Journal of Semantics, 11, pp. 83-101.
  3. Blackburn, P. (2000), “Representation, Reasoning, and Relational Structures: A Hybrid Logic Manifesto”, Logic Journal of the IGPL, 8 (3), pp. 339-365.
  4. Blackburn, P. y Seligman, J. (1998), “What are Hybrid Languages?”, en Kracht, M., de Rijke, M., Wansing, H. y Zakharyaschev, M. (eds.), Advances in Modal Logic, vol.1, Stanford, CA, CSLI Publications.
  5. Engelfriet, J. (1996), “Minimal Temporal Epistemic Logic”, Notre Dame Journal of Formal Logic, 37 (2), pp. 233-259.
  6. Fagin, R. y Halpern, J. Y. (1988), “Belief, Awareness and Limited Reasoning”, Artificial Intelligence, 34, pp. 39-76.
  7. Gabbay, D. M., Hodkinson, I. y Reynolds, M. (1994), Temporal Logic. Mathematical foundations and computational aspects, vol. 1, Oxford, Clarendon Press.
  8. Gabbay, D. M., Finger, M. y Reynolds, M. (2000), Temporal Logic. Mathematical foundations and computational aspects, vol. 2, Oxford, Oxford University Press.
  9. Goranko, V. (2000), “Computation Tree Logics and Temporal Logics with Reference Pointers”, Journal of Applied Non-classical Logics, 10 (3-4), pp. 221-242.
  10. Kraus, S. y Lehmann, D. (1988), “Knowledge, Belief and Time”, Theoretical Computer Science, 58, pp. 155-174.
  11. Lenzen, W. (2004), “Epistemic Logic”, en Niiniluoto, I., Sintonen, M. y Wolenski, J. (eds.), Handbook of Epistemology, Dordrecht, The Netherlands, Kluwer Academic Publishers, pp. 963-983.
  12. Meyer, J.-J. Ch. (2001), “Epistemic Logic”, en Goble, L. (ed.), The Blackwell Guide to Philosophical Logic, Oxford, Blackwell Publishers, pp. 183-202.
  13. Meyer, J.-J. Ch. y Van der Hoek, W. (1995), Epistemic Logic for AI and Computer Science, Cambridge, Cambridge University Press.
  14. Prior, A. (1967), Past, Present and Future, Oxford, Oxford UniversityPress.
  15. Sack, J. (2007), Adding a Temporal Logic to Dynamic Epistemic Logic. Tesis doctoral presentada en Indiana University.