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Foundations of Deductive Databases and Logic Programming
book

Foundations of Deductive Databases and Logic Programming

by Jack Minker
May 2014
Intermediate to advanced content levelIntermediate to advanced
752 pages
35h 3m
English
Morgan Kaufmann
Content preview from Foundations of Deductive Databases and Logic Programming
Chapter 15: Unification Revisited
611
It follows from
(1) and (2)
that
lim size(lca
{t
x
, t
2
,... ,t
n
} )
n—-oo
exists
and
will
be
found after
a
finite time.
Thus from
(3) it
follows that, modulo
~,
lim lca{t
v
t
v
...j
n
)
exists
and
will also
be
found after
a
finite time. Hence
the lea for an
infinite
set
can
be
found after
a
finite time using
the
Anti-unification Algorithm
as
lca{t
v
ί
2
,...,ί
Λ
,...
} = lim
lca{t
v
t
2
,...,t
n
}
= lim
λ(λ(...λ(ί
ρ
t
2
),...),t
n
)
η—-oo
n—-oc
LEMMA
8
If
the
Herbrand universe
is
non-trivial, then term
t is an lea of its
ground
in-
stances.
Proof:
The
proof
is by
induction
on the
number
of
variables
η in t. For η = 0
the resul ...
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Publisher Resources

ISBN: 9781483221120