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## Re: [ontolog-forum] Probabilistic Ontologies

 To: "[ontolog-forum] " Kathryn Blackmond Laskey Mon, 18 Jun 2007 00:36:56 -0400
 ```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: >Kathy, > >What I was asking is how a language such as IKL, which is a >superset of FOL that also supports metalevel statements, could >be used to represent the kinds of operations required for >probability models. > >> What you describe is far too simplistic. It's nearly impossible >> to create a probability model that way that's not either utterly >> simplistic or inconsistent. > >I used a very simple example, but the IKL mechanisms can be used >to support metalevel statements about propositions, the structural >components of propositions, their relationships to numerical >values, and the operations on those values. > >> Over the past several decades, statisticians and computer >> scientists have learned a great deal about how to represent >> probabilistic knowledge. > >I'm sure they have, but the IKL mechanisms can support those >representations. Anything that can be defined in PR-OWL or >BayesOWL can be defined in IKL plus much, much more. Numerical >functions of any kind can be defined in the Horn-clause subset >of IKL, which is a very efficient superset of OWL. > >> Sophisticated probability can be thought of as having two parts: >> the structural and the numerical. The structural part represents: >> (1) a set of random variables (uncertain features or relationships); >> (2) the possible values each random variable can take on); and >> (3) conditional dependency relationships. > >That could be represented in IKL. > >> For example, suppose we are trying to identify aircraft using radar >> reports. Consider two entities, a flying object and a sensor. We >> have two random variables: ObjectType and SensorReport. The possible >> values of each of these are {FighterAircraft, OtherAircraft, Bird}. >> The probability distribution for SensorReport depends on ObjectType. > >Could you give a specific example of the representations that are >currently used (preferably in the usual math notation, not in OWL). > >John > > > >_________________________________________________________________ >Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ >Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ >Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx >Shared Files: http://ontolog.cim3.net/file/ >Community Wiki: http://ontolog.cim3.net/wiki/ >To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx >    (013) _________________________________________________________________ Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/ Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/ Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx Shared Files: http://ontolog.cim3.net/file/ Community Wiki: http://ontolog.cim3.net/wiki/ To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (014) ```
 Current Thread Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, (continued) Message not availableRe: [ontolog-forum] Two ontologies that are inconsistent but both needed, Pat Hayes Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Kathryn Blackmond Laskey Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Pat Hayes Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Smith, Barry Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Smith, Barry Re: [ontolog-forum] Two ontologies that are inconsistent but both needed, Conklin, Don Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey <= Re: [ontolog-forum] Probabilistic Ontologies, Pat Hayes Re: [ontolog-forum] Probabilistic Ontologies, Kathryn Blackmond Laskey Re: [ontolog-forum] Probabilistic Ontologies, Pat Hayes Re: [ontolog-forum] Probabilistic Ontologies, John F. Sowa Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Barker, Sean (UK) Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk Re: [ontolog-forum] Probabilistic Ontologies, Barker, Sean (UK) Re: [ontolog-forum] Probabilistic Ontologies, Waclaw Kusnierczyk