250 13 Local, Global and Glocal Knowledge Representation
ImplicationLink InheritanceLink $X animal EvaluationLink
PredicateNode: eat ListLink
\$X
ConceptNode: food
is AverageLink $X ImplicationLink InheritanceLink $X animal EvaluationLink PredicateNode: eat ListLink
\$X ConceptNode: food
The AverageLink invokes an estimation of the average TruthValue of the embedded expression (in this case an ImplicationLink) over all possible values of the variable $X. If there are type restrictions regarding the variable $X, these are taken into account in conducting the averaging. For AllLink and Exist s-Link may be used in the same places as AverageLink, with uncertain truth value semantics defined in PLN theory using third-order probabilities. There is also a ScholemLink used to indicate variable dependencies for existentially quantified variables, used in cases of multiply nested existential quantifiers.
EvaluationLink and MemberLink have overlapping semantics, allowing expression of the same conceptual/logical relationships in terms of predicates or sets, i.e.
EvaluationLink PredicateNode: eat ListLink $X ConceptNode: food
has the same semantics as
MemberLink ListLink $X ConceptNode: food ConceptNode: EatingEvents
The relation between the predicate "eat" and the concept "EatingEvents" is formally given by
ExtensionalEquivalenceLink ConceptNode: EatingEvents SatisfyingSetLink
PredicateNode: eal
In other words, we say that "EatingEvents" is the SatisfyingSet of the predicate "eat": it is the set of entities that satisfy the predicate "eat". Note that the truth values of MemberLink and EvaluationLink are fuzzy rather than probabilistic.
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