Firstly, we can represent that using term logic without any explicit
variables
construct 1 =
ImplicationLink
___ANDLink
______ PredicateNode isMale
______ PredicateNode isUnmarried
___PredicateNode isBachelor
It's just a relationship between functions (predicates being mathematical
functions from entities to truth values)
Or, with different semantics, we could say
construct 2 =
ForAllLink
___ VariableNode X_1
___ ImplicationLink
______ANDLink
_________ EvaluationLink (PredicateNode isMale) X_1
_________ EvaluationLink (PredicateNode isUnmarried) X_1
______EvaluationLink (PredicateNode isBachelor) X_1
The truth values of construct 1 and construct 2 are related by some nice
formulas involving third-order probabilities ;-)
ben
On Tue, Aug 12, 2008 at 5:29 AM, YKY (Yan King Yin) <
[EMAIL PROTECTED]> wrote:
> Hi Ben,
>
> Hope you don't mind providing more clarification...
>
> In first-order logic there may be a rule such as:
> male(X) ^ unmarried(X) -> bachelor(X)
>
> We can convert this to a probabilistic rule:
> P(bachelor(X) = true | male(X) = true, unmarried(X) = true ) = 1.0
> but note that this rule contains the variable X.
>
> In my architecture, if I encounter a query such as:
> "is John a bachelor?"
>
> I would have to construct a propositional (ie, 0th-order) Bayes net to
> answer that query. During the construction, I would instantiate the
> rule with the variable substitution { X / John }.
>
> In other words, in my architecture the KB is a collection of logical
> formulae that do *not* form a network. Bayes nets are constructed
> _on-the-fly_ to answer specific queries.
>
> I'm not sure if PLN follows a similar arrangement. How can you have
> everything represented as networks when some rules with variables can
> be instantiated as many instances?
>
> YKY
>
>
> -------------------------------------------
> agi
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--
Ben Goertzel, PhD
CEO, Novamente LLC and Biomind LLC
Director of Research, SIAI
[EMAIL PROTECTED]
"Nothing will ever be attempted if all possible objections must be first
overcome " - Dr Samuel Johnson
-------------------------------------------
agi
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