17 Mar 2005
CS 3243 - Logical Inference
35
Proof of completeness
nFC derives every
atomic sentence that is entailed by
KB (only for clauses in Horn form)
1.FC reaches a fixed point (the deductive
closure) where no new atomic sentences are derived
2.Consider the final
state as a model m, assigning true/false
to symbols
3.Every clause in the
original KB is true in m
a1 Ù … Ù ak Þ b
4.Hence m is a model
of KB
5.If KB╞ q, q is true in every model
of KB, including m