G53KRR 2008-2009 answers 1. (a) Give an inductive truth definition for first order logic, that is, define when an Summary: G53KRR-E1 G53KRR 2008-2009 answers 1. (a) Give an inductive truth definition for first order logic, that is, define when an interpretation M = (D, I) and an assignment µ satisfy a formula . Assume that is defined by the following grammar: = P(t1, . . . , tn) | ¬ | | x where terms ti are either variables or constants. (7 marks) Answer. Let [t]M,µ be the denotation of a term t in M under µ. For a variable x, [x]M,µ is µ(x) and for a constant a, [a]M,µ is I(a). Then M, µ |= P(t1, . . . , tn) iff [t1]M,µ, . . . , [tn]M,µ I(P) M, µ |= ¬ iff M, µ |= M, µ |= 1 2 iff M, µ |= 1 and M, µ |= 2. M, µ |= x iff for every assignment µ which differs from µ at most in the value for x, M, µ |= . (b) Consider the following set of sentences: S1 Andrew is the father of Bob. S2 Bob is the father of Chris. S3 Every grandfather is someone's father. S4 Andrew is a grandfather of Chris. Translate these sentences into first-order logic, using binary predicates Father Collections: Computer Technologies and Information Sciences