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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 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, be the denotation of a term t in M under . For a variable x,
[x]M, is (x) and for a constant a, [a]M, is I(a). Then
M, |= P(t1, . . . , tn) iff [t1]M,, . . . , [tn]M, I(P)
M, |= iff M, |=
M, |= 1 2 iff M, |= 1 and M, |= 2.
M, |= x iff for every assignment which differs from at most in the value
for x, M, |= .
(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

  

Source: Alechina, Natasha - School of Computer Science, University of Nottingham

 

Collections: Computer Technologies and Information Sciences