Special Section on Concept Oriented Knowledge Representation under UncertaintyNo Access

PROBABILISTIC ROLE MODELS AND THE GUARDED FRAGMENT

MANFRED JAEGER

Aalborg Universitet, Institut for Datalogi, Fredrik Bajers Vej 7, 9220 Aalborg Ø, Denmark

https://doi.org/10.1142/S0218488506003820Cited by:8 (Source: Crossref)

Abstract

We propose a uniform semantic framework for interpreting probabilistic concept subsumption and probabilistic role quantification through statistical sampling distributions. This general semantic principle serves as the foundation for the development of a probabilistic version of the guarded fragment of first-order logic. A characterization of equivalence in that logic in terms of bisimulations is given.

References

M. Abadi and J. Y. Halpern, Information and Computation 112, 1 (1994), DOI: 10.1006/inco.1994.1049. Crossref, Web of Science, Google Scholar
H. Andréka, I. Németi and J. van Benthem, Journal of Philosophical Logic 27, 217 (1998), DOI: 10.1023/A:1004275029985. Crossref, Web of Science, Google Scholar
F. Baader et al. (eds.) , The Description Logic Handbook ( Cambridge University Press , 2003 ) . Google Scholar
F. Bacchus , Representing and Reasoning With Probabilistic Knowledge ( MIT Press , 1990 ) . Google Scholar
G. Boole , Investigations of Laws of Thought on which are Founded the Mathematical Theories of Logic and Probabilities ( London , 1854 ) . Crossref, Google Scholar
H.-D. Ebbinghaus and J. Flum , Finite Model Theory , 2nd edn. , Perspectives in Mathematical Logic ( Springer Verlag , 1999 ) . Crossref, Google Scholar
R. Giugno and T. Lukasiewicz, P-shoq(d): A probabilistic extension of shoq(d) for probabilistic ontologies in the semantic web, Proceedings of the 8th European Conference on Logics in Artificial Intelligence (JELIA'02) (2002) pp. 86–97. Google Scholar
T. Hailperin, American Mathematical Monthly 72, 343 (1965). Crossref, Web of Science, Google Scholar
J. Halpern, Artificial Intelligence 46, 311 (1990). Crossref, Web of Science, Google Scholar
J. Heinsohn, Probabilistic description logics, Proceedings of the Tenth Annual Conference on Uncertainty in Artificial Intelligence (UAI-94) (1994) pp. 311–318. Google Scholar
M. Jaeger, Probabilistic reasoning in terminological logics, Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR94) (1994) pp. 305–316. Google Scholar
M. Jaeger, Probabilistic role models and the guarded fragment, Proceedings of IPMU-04 (2004) pp. 235–242. Google Scholar
D. Keller, A. Levy and A. Pfeffer, P-cassic: A tractable probabilistic description logic, Proceedings of the Fourteenth National Conference on Artificial Intelligence (AAAI-97) (1997) pp. 390–397. Google Scholar
K. Larsen and A. Skou, Compositional verification of probabilistic processes, Proceedings of the Third International Conference on Concurrency Theory (Concur-92) (1992) pp. 456–471. Google Scholar
K. G. Larsen and A. Skou, Information and Computation 94, 1 (1991), DOI: 10.1016/0890-5401(91)90030-6. Crossref, Web of Science, Google Scholar
R. Ng, IEEE Transactions on Knowledge and Data Engineering 9, 32 (1997), DOI: 10.1109/69.567045. Crossref, Web of Science, Google Scholar
N. Nilsson, Artificial Intelligence 28, 71 (1986), DOI: 10.1016/0004-3702(86)90031-7. Crossref, Web of Science, Google Scholar
Z. Ognjanovic and M. Raškovic, Theoretical Computer Science 247, 191 (2000), DOI: 10.1016/S0304-3975(98)00341-7. Crossref, Web of Science, Google Scholar
M. Otto, Annals of Pure and Applied Logic 130, 173 (2004), DOI: 10.1016/j.apal.2004.04.003. Crossref, Web of Science, Google Scholar
M. Y. Vardi, Automatic verification of probabilistic concurrent finite-state programs, Proceedings of the 26th IEEE Symposium on Foundations of Computer Science (1985) pp. 327–338. Google Scholar