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On AGM for Non-Classical Logics

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Abstract

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

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References

  1. Alchourrón, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change. Journal of Symbolic Logic, 50(2), 510–530.

    Article  Google Scholar 

  2. Alchourrón, C., & Makinson, D. (1982). On the logic of theory change: Contraction functions and their associated revision functions. Theoria, 48, 14–37.

    Article  Google Scholar 

  3. Alechina, N., Jago, M., & Logan, B. (2005). Resource-bounded belief revision and contraction. In M. Baldoni, U. Endriss, A. Omicini, & P. Torroni (Eds.), Proceedings of the third international workshop on declarative agent languages and technologies (DALT 2005) (Vol. 31, pp. 118–131).

  4. Anderson, A. R., & Belnap, N. D. (1963). First degree entailments. Mathematische Annalen, 149(4), 302–319.

    Article  Google Scholar 

  5. Anderson, A. R., & Belnap, N. D. (1975). Entailment: The logic of relevance and necessity (Vol. 1). Princeton University Press.

  6. Booth, R., Meyer, T., & Varzinczak, I. J. (2009). New steps in propositional Horn contraction. In Proceedings of the international joint conference of artificial intelligence (IJCAI). Pasadena.

  7. Booth, R., Meyer, T., Varzinczak, I. J., & Wassermann, R. (2010). A contraction core for Horn belief change: Preliminary report. In Proceedings of the international workshop on non-monotonic reasoning (NMR).

  8. Calvanese, D., Kharlamov, E., Nutt, W., & Zheleznyakov, D. (2010). Evolution of DL-lite knowledge bases. In Proceedings of the 9th international semantic Web conference (ISWC 2010).

  9. Chopra, S., Georgatos, K., & Parikh, R. (2001). Relevance sensitive non-monotonic inference on belief sequences. Journal of Applied Non-Classical Logics, 11(1–2), 131–150.

    Article  Google Scholar 

  10. Chopra, S., & Parikh, R. (2000). Relevance sensitive belief structures. Annals of Mathematics and Artificial Intelligence, 28(1–4), 259–285.

    Article  Google Scholar 

  11. Chopra, S., Parikh, R., & Wassermann, R. (2001). Approximate belief revision. Logic Journal of the IGPL, 9(6), 755–768.

    Article  Google Scholar 

  12. da Costa, N. C. A., & Bueno, O. (1998). Belief change and inconsistency. Logique & Analyse, 41(161–163), 31–56.

    Google Scholar 

  13. da Costa, N. C. A. (1963). Calculs propositionnels pour les systémes formels inconsistants. Comptes Rendus d’Academie des Sciences de Paris, 257, 3790–3793.

    Google Scholar 

  14. Delgrande, J. P. (2008). Horn clause belief change: Contraction functions. In G. Brewka, & J. Lang (Eds.), Principles of knowledge representation and reasoning (KR2008) (pp. 156–165).

  15. Delgrande, J. P., & Wassermann, R. (2010). Horn clause contraction functions: Belief set and belief base approaches. In Principles of knowledge representation and reasoning (KR2010).

  16. Finger, M., & Wassermann, R. (2004). Approximate and limited reasoning: Semantics, proof theory, expressivity and control. Journal of Logic And Computation, 14(2), 179–204.

    Article  Google Scholar 

  17. Flouris, G. (2006). On belief change and ontology evolution. Ph.D. thesis, University of Crete.

  18. Flouris, G., Plexousakis, D., & Antoniou, G. (2004). Generalizing the AGM postulates: Preliminary results and applications. In Proceedings of the 10th international workshop on non-monotonic reasoning (NMR 2004) (pp. 171–179).

  19. Flouris, G., Plexousakis, D., & Antoniou, G. (2005). On applying the AGM theory to DLs and OWL. In: Proceedings of the international semantic Web Conference (pp. 216–231).

  20. Fuhrmann, A. (1991). Theory contraction through base contraction. Journal of Philosophical Logic, 20, 175–203.

    Article  Google Scholar 

  21. Gärdenfors, P. (1988). Knowledge in flux—Modeling the dynamics of epistemic states. MIT Press.

  22. Gärdenfors, P., & Rott, H. (1995). Belief revision. In Handbook of logic in artificial intelligence and logic programming (Vol. IV, Chapt. 4.2). Oxford University Press.

  23. Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17, 157–170.

    Article  Google Scholar 

  24. Halaschek-Wiener, C., & Katz, Y. (2006). Belief base revision for expressive description logics. In Proceedings of the OWLED*06 workshop on OWL: Experiences and directions.

  25. Hansson, S. O. (1992). A dyadic representation of belief. In P. Gärdenfors (Ed.), Belief revision. Cambridge tracts in theoretical computer science (Vol. 29, pp. 89–121). Cambridge University Press.

  26. Hansson, S. O. (1992). Reversing the Levi identity. Journal of Philosophical Logic, 22, 637–639.

    Article  Google Scholar 

  27. Hansson, S. O. (1994). Kernel contraction. Journal of Symbolic Logic, 59, 845–859.

    Article  Google Scholar 

  28. Hansson, S. O. (1999). A textbook of belief dynamics. Kluwer Academic Press.

  29. Hansson, S. O., & Wassermann, R. (2002). Local change. Studia Logica, 70(1), 49–76.

    Article  Google Scholar 

  30. Jaśkowski, S. (1969). Propositional calculus for contradictory deductive systems. Studia Logica, 24, 143–157.

    Article  Google Scholar 

  31. Katsuno, H., & Mendelzon, A. O. (1992). On the difference between updating a knowledge base and revising it. In P. Gärdenfors (Ed.), Belief revision. Cambridge tracts in theoretical computer science (Vol. 29, pp. 183–203). Cambridge University Press.

  32. Lakemeyer, G., & Lang, W. (1996). Belief revision in a nonclassical logic. In G. Görz, & S. Hölldobler (Eds.), KI-96: Advances in artificial intelligence. Lecture notes in computer science (Vol. 1137, pp. 199–211). Berlin: Springer.

    Google Scholar 

  33. Levesque, H. (1984). A logic of implicit and explicit belief. In Proceedings of AAAI-84.

  34. Makinson, D. (2009). Propositional relevance through letter-sharing. Journal of Applied Logic, 7(4), 377–387. Special Issue: Formal models of belief change in rational agents.

    Article  Google Scholar 

  35. Mares, E. D. (2002). A paraconsistent theory of belief revision. Erkenntnis, 56(2), 229–246.

    Article  Google Scholar 

  36. Nebel, B. (1990). Reasoning and revision in hybrid representation systems. Lecture notes in artificial intelligence (Vol. 422). Berlin: Springer.

    Google Scholar 

  37. Parikh, R. (1996). Beliefs, belief revision and splitting languages. In Proceedings of Itallc-96.

  38. Parsia, B. (2009). Topic-sensitive belief revision. Ph.D. thesis, University of Maryland.

  39. Priest, G. (2001). Paraconsistent belief revision. Theoria, 67(3), 214–228.

    Article  Google Scholar 

  40. Restall, G., & Slaney, J. (1995). Realistic belief revision. In M. D. Glas, & Z. Pawlak (Eds.), Proceedings of the second world conference on the fundamentals of artificial intelligence (pp. 367–378).

  41. Ribeiro, M. M., & Wassermann, R. (2006). First steps towards revising ontologies. In Proceedings of the second workshop on ontologies and their applications (WONTO).

  42. Ribeiro, M. M., & Wassermann, R. (2009). AGM revision in description logics. In Proceedings the IJCAI workshop on automated reasoning about context and ontology evolution (ARCOE).

  43. Ribeiro, M. M., & Wassermann, R. (2009). Base revision for ontology debugging. Journal of Logic and Computation, 19(5), 721–743.

    Article  Google Scholar 

  44. Ribeiro, M. M., & Wassermann, R. (2010). More about AGM revision in description logics. In Proceedings the ECAI workshop on automated reasoning about context and ontology evolution (ARCOE).

  45. Rodrigues, O. T. (1997). A methodology for iterated information change. Ph.D. thesis, Imperial College, University of London.

  46. Rott, H. (2001). Change, choice and inference: A study of belief revision and nonmonotonic reasoning. Oxford University Press.

  47. Schaerf, M., & Cadoli, M. (1995). Tractable reasoning via approximation. Artificial Intelligence, 74(2), 249–310.

    Article  Google Scholar 

  48. Tanaka, K. (2005). The AGM theory and inconsistent belief change. Logique et analyse, 48(189–192), 113–150.

    Google Scholar 

  49. Wassermann, R. (2001). On structured belief bases. In H. Rott, & M.-A. Williams (Eds.), Frontiers in belief revision. Kluwer.

  50. Wassermann, R. (2003). Generalized change and the meaning of rationality postulates. Studia Logica, 73(2), 299–319.

    Article  Google Scholar 

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  1. Department of Computer Science, Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil

    Renata Wassermann

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  1. Renata Wassermann
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Wassermann, R. On AGM for Non-Classical Logics. J Philos Logic 40, 271–294 (2011). https://doi.org/10.1007/s10992-011-9178-2

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