Database Reference
In-Depth Information
Just as such a tree requires some tree-walking algorithm to get from a higher
node to a lower node or from a lower node to a higher node, a schema like 6.5.5
requires DBS inferences to utilize the content of the hierarchy for reasoning.
For example, an inference for downward traversal should allow the agent to
infer that
food
may be instantiated by apples, pairs, salad, or steak, while an
inference for upward traversal should infer that an apple, for example, instan-
tiates
food
.
23
Given that semantic hierarchy relations abound in the lexicon, we derive the
inferences for their upward and downward traversal automatically by means
of a meta-inference which takes a schema like 6.5.5 as input and derives the
associated inferences for upward and downward traversal:
6.5.7 M
ETA
-
INFERENCE DERIVING
down
AND
up
INFERENCES
antecedent
consequent 1
consequent 2
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
down
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
up
⎡
⎣
⎤
⎦
noun: HT
fnc:
β
prn: K
noun: HT
fnc:
β
prn: K
noun:
α
fnc: (
β
K)
prn: K+M
noun:
α
fnc:
β
prn: K
noun: HT
fnc: (
β
K)
prn: K+M
=
⇒
where HT
{A, B, C, D, ...} where
α
{A, B, C, D, ...} where
α
{A, B, C, D, ...}
The variable HT stands for a higher-term constant, e.g.,
food
, while the vari-
ables A, B, C, D, ..., stand for the instantiation constants, e.g., apple, pear,
salad, steak. Other examples of higher term constants are
mammal
,whichis
instantiated by dogs, cats, and mice;
vehicle
, which is instantiated by cars,
trucks, and buses;
water
, which is instantiated by ocean, lake, and river; and
so on. They may all be derived automatically in the same way as is the higher
term
food
, as shown in 6.5.3 - 6.5.5.
Application of the meta-inference 6.5.7 to the
food
proplet 6.5.5 results in
the following inference for downward traversal:
6.5.8 A
PPLYING META
-
INFERENCE
6.5.7
TO DERIVE
down
INFERENCE
antecedent
consequent
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
noun: HT
fnc:
β
prn: K
noun: HT
fnc:
β
prn: K
noun:
α
fnc: (
β
K)
prn: K+M
=
⇒
down
where HT
{A, B, C, D, ...}
where
α
{A, B, C, D,...}
⇑
matching and binding
⇓
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
down
⎡
⎣
⎤
⎦
noun: food
fnc: eat
prn: K
noun: food
fnc:
β
prn: K
noun:
α
fnc: (
β
K)
prn: K+M
where food
{apple, pear, salad, steak} where
α
{apple, pear, salad, steak}
While meta-inferences are applied to pattern proplets with restricted higher
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