To: |
"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx> |
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From: |
Kathryn Blackmond Laskey <klaskey@xxxxxxx> |

Date: |
Mon, 18 Jun 2007 00:36:56 -0400 |

Message-id: |
<p0611041ec29b366a566b@[192.168.0.103]> |

John, (01) Yes, the kinds of representations that are needed could be encoded as meta-level statements in IKL. It's more complex than simply attaching probabilities to logical statements, but it's straightforward. (02) Paulo Costa and I recently put together a simple example of pizzas and wines. See http://ite.gmu.edu/~klaskey/PizzaWine/PizzaWineExample.xhtml. (03) Consider for example the Pizza Base MFrag, a fragment of a Bayesian network that represents the pizza bases a customer is likely to choose given his/her choice(s) of wine. (04) We have: (05) (1) Context random variables: These are constraints that have to be satisfied for the probability distributions to make sense. They are IsA(Pizza,p), IsA(Wine,w), and ServedWith(w,p). (06) (2) Resident random variable: This is a random variable whose distribution is defined in the MFrag. In this case, we have one resident random variable, PizzaBase(p), with possible values ThinAndCrispyBase and DeepPanBase. (07) (3) Input random variables: These are random variables that influence the probability of the resident random variable. In this case, the pizza base is influenced by WineBody(w) and WineFlavor(w). (08) (4) Local distributions: An instance of the resident random variable will created for each pizza instance in the situation about which we are reasoning. To construct its probability distribution, we need a function that maps the WineBody and WineFlavor of all the wine instances satisfying the ServedWith relation to a probability distribution on the values ThinAndCrispyBase and DeepPanBase. (09) So this MFrag says that the probability distribution for the type of pizza base a customer is likely to order depends on the body and flavor of the wine(s) that are served with it. The MFrag defines a function for mapping wine and body flavors to probability distributions on pizza bases. (010) All this could be represented by meta-level statements in IKL. It would not be too difficult to write an upper ontology for MFrags in IKL, similarly to the OWL upper ontology we built for PR-OWL. We might call it PRIKL. :-) (011) Kathy (012) At 7:44 AM -0400 6/17/07, John F. Sowa wrote: > |

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