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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
606 Lassez, Mäher, and Marriott
PROPOSITION
15
Substitution μ is an mgu iff ν Ε αοηιαΐη(μ) Π range{\i) =^>
E(JC
ν) Ε μ .
Proof:
Let θ be an equivalent idempotent mgu, then μ = θοα where α =
{JC
χμ:χ Ε domain^), χ ^ domain^)}. Now, ν Ε άοηιαΐη(μ) Π range{p) implies
that ν Ε range(a). There are two cases: If ν £ rangera) then, since ν Ε
domain(\L),
we must have ν Ε domain(a). Thus, the ν in ranged) does not
contribute to μ, and so ν Ε range(a). If ν ^ range(Q) then, since ν E
range(\L),
we must have ν Ε range(a). From the previous proposition, α has the form {x
x
Vj,...,jc
m
v
m
} and so
3(JC
*-v)6a and hence
3(JC
ν) Ε μ.
Consequently not al ...
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Publisher Resources

ISBN: 9781483221120