On the decidability and complexity of reasoning about only knowing

Artificial Intelligence

Volumn 116, Issue 1-2, 2000, Pages 193-215

  Rosati, Riccardo ^a  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTABILITY AND DECIDABILITY; COMPUTATIONAL COMPLEXITY; KNOWLEDGE REPRESENTATION; POLYNOMIALS;

EPISTEMIC LOGICS; LEVESQUE LOGIC; NONMONOTONIC REASONING;

ARTIFICIAL INTELLIGENCE;

EID: 0033881953     PISSN: 00043702     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0004-3702(99)00083-1     Document Type: Article

References (28)

1. Chen J. The logic of only knowing as a unified framework for nonmonotonic reasoning. Fundamenta Informaticae. 21:1994;205-220.
2. Donini F.M., Nardi D., Rosati R. Ground nonmonotonic modal logics. J. Logic and Computation. 7:(4):1997;523-548.
3. Eiter T., Gottlob G. Reasoning with parsimonious and moderately grounded expansions. Fundamenta Informaticae. 17:(1, 2):1992;31-54.
4. Eiter T., Gottlob G. Propositional circumscription and extended closed world reasoning are Π^p_2 -complete. Theoret. Comput. Sci. 114:1993;231-245.
5. Gottlob G. Complexity results for nonmonotonic logics. J. Logic and Computation. 2:1992;397-425.
6. Gottlob G. NP trees and Carnap's modal logic. J. ACM. 42:(2):1995;421-457.
7. Halpern J.Y., Lakemeyer G. Levesque's axiomatization of only knowing is incomplete. Artificial Intelligence. 74:(2):1995;381-387.
8. Halpern J.Y., Lakemeyer G. Multi-agent only knowing. Proc. 6th Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-96) :1996;Morgan Kaufmann, San Mateo, CA.
9. Halpern J.Y., Moses Y. Towards a theory of knowledge and ignorance: Preliminary report. Apt K. Logic and Models of Concurrent Systems. 1985;Springer, Berlin.
10. Halpern J.Y., Moses Y. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence. 54:1992;319-379.
11. Johnson D.S. A catalog of complexity classes. van Leuven J. Handbook of Theoretical Computer Science, Vol. A. 1990;Elsevier Science, North-Holland, Amsterdam. Chapter 2.
12. Kaminski M. Embedding a default system into nonmonotonic logics. Fundamenta Informaticae. 14:1991;345-354.
13. Lakemeyer G. Limited reasoning in first-order knowledge bases with full introspection. Artificial Intelligence. 84:1996;209-255.
14. Lakemeyer G. Only knowing in the situation calculus. Aiello L.C., Doyle J., Shapiro S.C. Proc. 5th International Conference on the Principles of Knowledge Representation and Reasoning (KR-96) :1996;14-25 Morgan Kaufmann, Los Altos, CA.
15. Lakemeyer G., Levesque H.J. A tractable knowledge representation service with full introspection. Proc. 2nd Conference on Theoretical Aspects of Reasoning about Knowledge (TARK-88) :1988;145-159 Morgan Kaufmann, Los Altos, CA.
16. Lakemeyer G., Levesque H.J. AOL: A logic of acting, sensing, knowing, and only knowing. Proc. 6th International Conference on the Principles of Knowledge Representation and Reasoning (KR-98). 1998;316-327 Morgan Kaufmann, Los Altos, CA.
17. Levesque H.J. Foundations of a functional approach to knowledge representation. Artificial Intelligence. 23:1984;155-212.
18. Levesque H.J. All I know: A study in autoepistemic logic. Artificial Intelligence. 42:1990;263-310.
19. Lifschitz V. Minimal belief and negation as failure. Artificial Intelligence. 70:1994;53-72.
20. Marek W., Truszczyński M. Nonmonotonic Logics - Context-Dependent Reasoning. 1993;Springer, Berlin.
21. Moore R.C. Semantical considerations on nonmonotonic logic. Artificial Intelligence. 25:1985;75-94.
22. Niemeläa I. On the decidability and complexity of autoepistemic reasoning. Fundamenta Informaticae. 17:(1, 2):1992;117-156.
23. Reiter R. What should a database know? J. Logic Programming. 14:1990;127-153.
24. Rosati R. Reasoning with minimal belief and negation as failure: Algorithms and complexity. Proc. AAAI-97, Providence, RI. 1997;430-435.
25. Rosati R. Reasoning about minimal knowledge in nonmonotonic modal logics. J. Logic, Language and Information. 8:(2):1999;187-203.
26. Schwarz G., Truszczyński M. Minimal knowledge problem: A new approach. Artificial Intelligence. 67:1994;113-141.
27. Shoham Y. Nonmonotonic logics: Meaning and utility. Proc. IJCAI-87, Milan, Italy :1987;388-392.
28. Wolter F., Zakharyaschev M. Decidable fragments of first-order modal logics. Available at www.informatik.uni-leipzig.de/ ~ wolter . 1999.