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Unformatted text preview: ?x.p i.e., for any M and ais M {ai/xi}G implies M {ai/xi}?x.p Yes, t can be any term. Are the Rules Sound? (4/4) ?x.p p q q ?e Can q be anything? qs free ivar should not be free in p. Soundness: G q implies G q. I.H. G {t/x}p and G,p q i.e., for any M and ais M {ai/xi}G implies M {ai/xi}({t/x}p) and M {ai/xi}(G,p) implies M {ai/xi}q T.S. G q i.e., for any M and ais M {ai/xi}G implies M {ai/xi}q Proof/Deduction/Inference Examples (1/2) !x.P(x)>Q(x) !x.P(x)>!x.Q(x) !x.(P(x)>Q(x)) !x.P(x) P(x)>Q(x) P(x) Q(x) !x.Q(x) !x.P(x)>!x.Q(x) Proof/Deduction/Inference Examples (2/2) P(x)>!x.Q(x) !y.(P(x)>Q(y)) !y.(P(x)>Q(y)) P(x)>!x.Q(x) P(x) Q(y) !x.Q(x) P(x)>Q(y) (?x.p) !x.( p) (?x.p) !x.( p) p p {x/x}p ?x.p Soundness/Completeness the deduction rules for the firstorder predicate logic are sound and complete every provable formula is true/valid every true/valid formula is provable p <=> p...
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This note was uploaded on 07/05/2010 for the course E 45 taught by Professor Gronsky during the Fall '08 term at University of California, Berkeley.
 Fall '08
 GRONSKY

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