3 Mar 2004
CS3243 - Inference
7
Reduction contd.
Theorem: Herbrand (1930). If a sentence α is entailed by an FOL KB, it is
entailed by a finite subset of the propositionalized KB
Idea: For n = 0 to ∞ do
create a
propositional KB by instantiating with depth-n terms
see if α is entailed by
this KB
Problem: works if α is entailed, loops if α is not
entailed
Theorem: Turing (1936), Church (1936) Entailment for FOL
is
semidecidable (algorithms exist that say yes to every entailed sentence, but no algorithm exists that also says no to every non-entailed sentence.)
semidecidable (algorithms exist that say yes to every entailed sentence, but no algorithm exists that also says no to every non-entailed sentence.)