Modal Semirings with Operators for Knowledge Representation

Kim Solin

2013

Abstract

Modal semirings are combined with modal algebra (Boolean algebra with operators) to form modal semirings with operators. In turn, these are extended with a revision operator and used for knowledge representation.

References

  1. Aboul-Hosn, K. and Kozen, D. (2006). KAT-ML: an interactive theorem prover for Kleene algebra with tests. Journal of Applied Non-Classical Logics, 16(1-2):9- 34.
  2. Alchourrón, C., Gärdenfors, P., and Makinson, D. (1985). On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2):510-530.
  3. Baltag, A., Coecke, B., and Sadrzadeh, M. (2005). Algebra and sequent calculus for epistemic actions. Electronic Notes in Theoretical Computer Science, 126:27-52.
  4. Baltag, A., Coecke, B., and Sadrzadeh, M. (2007). Epistemic actions as resources. Journal of Logic and Computation, 17(3):555-585.
  5. Baltag, A. and Sadrzadeh, M. (2006). The algebra of multiagent dynamic belief revision. Electronic Notes in Theoretical Computer Science, 157(4):37-56.
  6. Cantwell, J. (2000). Non-Linear Belief Revision: Foundations and Applications. Acta Universitatis Upsaliensis. Dissertation.
  7. Desharnais, J., Möller, B., and Struth, G. (2006). Kleene algebra with domain. ACM Transactions on Computational Logic, 7(4):798-833.
  8. Dijkstra, E. W. (1976). Prentice-Hall.
  9. Foster, S. and Struth, G. (2012). Automated analysis of regular algebra. In Gramlich, B., Miller, D., and Sattler, U., editors, IJCAR, volume 7364 of Lecture Notes in Computer Science, pages 271-285. Springer.
  10. Harel, D., Kozen, D., and Tiurun, J. (2000). Dynamic Logic. MIT Press.
  11. Höfner, P. and Struth, G. (2007). Automated reasoning in Kleene algebra. In Pfenning, F., editor, CADE, volume 4603 of Lecture Notes in Computer Science, pages 279-294. Springer.
  12. Jónsson, B. and Tarski, A. (1951). Boolean algebra with operators. Part I. American Journal of Mathematics, 73(4):891-939.
  13. Jónsson, B. and Tarski, A. (1952). Boolean algebra with operators. Part II. American Journal of Mathematics, 74(1):127-939.
  14. Kozen, D. (1994). A completeness theorem for Kleene algebras and the algebra of regular events. Inf. Comput., 110(2):366-390.
  15. Kozen, D. (1997). Kleene algebra with tests. ACM Transactions on Programming Languages and Systems, 19(3):427-443.
  16. Lemmon, E. J. (1966a). Algebraic semantics for modal logics I. The Journal of Symbolic Logic, 31(1):46-65.
  17. Lemmon, E. J. (1966b). Algebraic semantics for modal logics II. The Journal of Symbolic Logic, 31(1):191-218.
  18. Möller, B. (2008). Knowledge and games in modal semirings. In Berghammer, R., Möller, B., and Struth, G., editors, RelMiCS, volume 4988 of Lecture Notes in Computer Science, pages 320-336. Springer.
  19. Panangaden, P. and Sadrzadeh, M. (2010). Learning in a changing world, an algebraic modal logical approach. In Johnson, M. and Pavlovic, D., editors, AMAST, volume 6486 of Lecture Notes in Computer Science, pages 128-141. Springer.
  20. Segerberg, K. (1999). Two traditions in the logic of belief: bringing them together. In Ohlback, H. and Reyle, U., editors, Logic, Language and Reasoning, pages 134- 147. Kluwer.
  21. Solin, K. (2010). A sketch of a dynamic epistemic semiring. Inf. Comput., 208(5):594-604.
  22. van Ditmarsch, H., van der Hoek, W., and Kooi, B. (2007). Dynamic Epistemic Logic. Springer.
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Paper Citation


in Harvard Style

Solin K. (2013). Modal Semirings with Operators for Knowledge Representation . In Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART, ISBN 978-989-8565-39-6, pages 197-202. DOI: 10.5220/0004181001970202


in Bibtex Style

@conference{icaart13,
author={Kim Solin},
title={Modal Semirings with Operators for Knowledge Representation},
booktitle={Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},
year={2013},
pages={197-202},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004181001970202},
isbn={978-989-8565-39-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 5th International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,
TI - Modal Semirings with Operators for Knowledge Representation
SN - 978-989-8565-39-6
AU - Solin K.
PY - 2013
SP - 197
EP - 202
DO - 10.5220/0004181001970202