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The Basics |
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Arity |
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Argument Types |
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Second-Order Predicates |
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More on Functions |
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Sometimes we want to make statements about
predicates themselves. |
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This requires “second-order” predicates, which can
take predicates as arguments. |
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Examples :
#$arg1Isa, #$arity, #$isa |
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Thus
in (#$arity #$mother 2), |
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#$arity
takes the predicate #$mother as its first argument. |
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Some second-order predicates are used to relate
CycL predicates to one another within a predicate hierarchy . . . |
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#$genlPreds |
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(#$isa #$genlPreds #$BinaryPredicate) |
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(#$arg1Isa
#$genlPreds #$Predicate) |
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(#$arg2Isa
#$genlPreds #$Predicate) |
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(#$genlPreds ?NARROW-PRED ?WIDE-PRED) means that
?NARROW-PRED is a restricted version of ?WIDE-PRED |
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Any arguments of which ?NARROW-PRED is true are
also ones of which ?WIDE-PRED
is true. |
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Predicates related by #$genlPreds can be any
arity, as
long as they both have the same arity. |
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#$genlPreds
(continued) |
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(#$genlPreds #$biologicalMother #$biologicalParents) |
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is (#$implies |
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(#$biologicalMother ?X ?Y) |
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(#$biologicalParents ?X ?Y)) |
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(#$genlPreds #$createdBy #$startsAfterStartingOf) |
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is (#$implies |
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(#$createdBy
?X ?Y) |
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(#$startsAfterStartingOf ?X
?Y)) |
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#$genlInverse |
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(#$genlInverse
?NARROW-PRED ?WIDE-PRED-INV)
means that |
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?NARROW-PRED
is a restricted version of ?WIDE-PRED-INV, |
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with argument
order reversed. |
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#$genlInverse |
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(#$genlInverse
?NARROW-PRED ?WIDE-PRED-INV)
means that |
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?NARROW-PRED
is a restricted version of ?WIDE-PRED-INV, |
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with argument
order reversed. |
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How would this be expressed in a rule ? |
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#$genlInverse |
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(#$genlInverse
?NARROW-PRED ?WIDE-PRED-INV)
means that ?NARROW-PRED is a restricted
version of ?WIDE-PRED-INV, with argument
order reversed. |
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How would this be expressed in a rule ? |
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(#$implies |
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(?NARROW-PRED ?ARG1 ?ARG2) |
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(?WIDE-PRED-INV ?ARG2 ?ARG1)) |
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?NARROW-PRED and ?WIDE-INV-PRED must be binary predicates. |
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Example
: (#$genlInverse #$customers #$suppliers) |
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#$negationPreds |
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(#$negationPreds ?PRED ?NEG-PRED) means that |
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if (?PRED
?ARG1 … ?ARGN) |
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then not (?NEG-PRED ?ARG1 … ?ARGN) |
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?PRED
and ?NEG-PRED can be of any arity, as long as |
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they
both have the same arity. |
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Example
: (#$negationPreds #$owns
#$rents) |
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#$negationInverse |
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(#$negationInverse
?PRED ?NEG-PRED-INV) means that |
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if (?PRED ?ARG1
?ARG2) |
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then not (?NEG-PRED-INV ?ARG2 ?ARG1) |
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?PRED
and ?NEG-PRED-INV must be binary predicates. |
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Example: (#$negationInverse #$subordinates #$subordinates) |
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Second-Order predicates can be used to express
relations between predicates |
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The four predicates discussed were: |
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#$genlPreds |
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#$genlInverse |
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#$negationPreds |
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#$negationInverse |
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Notes