Nilsson's Probabilistic Entailment Extended to DempsterShafer Theory
Mary McLeish
Abstract:
Probabilistic logic has been discussed in a recent paper by N. Nilsson [12]. An entailment scheme is proposed which can predict the probability of an event when the probabilities of certain other connected events are known. This scheme involves the use of a maximum entropy method proposed by P. Cheeseman in [3]. The model uses vectors which represent certain possible states of the world. Only consistent such vectors are entered into the probability scheme. As a result, entailment does not always yield an acceptable result and cannot be applied to real situations which could arise. This paper investigates a technique to overcome this problem, which involves extending the idea of probabilistic logic and the maximum entropy approach to DempsterShafer theory. A new entailment scheme for belief functions is used which produces welldefined results, even when only "consistent" worlds are being considered. The paper also reconsiders an earlier attempt by the author [6,7] to model default reasoning (and subsequent nonmonotonicity) by adding inconsistent vectors to Nilsson's model. In the extended setting, more sensible entailment values are obtained than in the previous work.
Keywords: Probabilistic Logic, Maximum Entropy Method, DempsterShafer theory
Pages: 2334
PS Link:
PDF Link: /papers/87/p23mcleish.pdf
BibTex:
@INPROCEEDINGS{McLeish87,
AUTHOR = "Mary McLeish
",
TITLE = "Nilsson's Probabilistic Entailment Extended to DempsterShafer Theory",
BOOKTITLE = "Uncertainty in Artificial Intelligence 3 Annual Conference on Uncertainty in Artificial Intelligence (UAI87)",
PUBLISHER = "Elsevier Science",
ADDRESS = "Amsterdam, NL",
YEAR = "1987",
PAGES = "2334"
}

