Unformatted text preview: P ( k ) holds, for some arbitrary k , about which we know nothing, other than that it belongs to the domain D . The term k is sometimes called an eigenvariable . An important constraint on this rule is that k cannot appear anywhere in P (or in any formula of the proof below the point where this rule is used. Example Proof: (1) ∃ x.likes ( x,fritos ) ( premise ) (2) ∀ x.likes ( x,fritos ) → likes ( x,doritos ) ( premise ) (3) likes ( b,fritos ) ( ∃-elim-1) (4) likes ( b,fritos ) → likes ( b,doritos ) ( ∀-elim-2) (5) likes ( b,doritos ) ( modusponens-3 , 4) (6) ∃ x.likes ( x,doritos ) ( ∃-intro-5)...
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- Fall '08
- Pennsylvania State University, Modus ponens, Penn State University, Rule of inference, universally quantiﬁed formula