18 and 25 Feb 2004
CS 3243 - Logical Agents
50
Proof of completeness
nFC derives every
atomic sentence that is entailed by
KB
1.FC reaches a fixed point 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