Answers G53KRR 2009-10 1. (a) Express the following sentences in first-order logic, using unary predicates Fragile, Summary: G53KRR-E1 Answers G53KRR 2009-10 1. (a) Express the following sentences in first-order logic, using unary predicates Fragile, Break, Fall, TennisBall. S1 Fragile things break if they fall (2 marks) S2 Tennis balls are not fragile (2 marks) S3 Tennis balls don't break if they fall (2 marks) Answer S1 x(Fragile(x) Fall(x) Break(x)) S2 x(TennisBall(x) ¬Fragile(x)) S3 x(TennisBall(x) Fall(x) ¬Break(x)) (b) Give a definition of logical entailment for first-order logic, that is, what it means for a set of sentences S to logically entail a sentence A. (4 marks) Answer S logically entails A if for every interpretation I, if I makes true all sen- tences in S, it also makes A true. (c) Do sentences S1 and S2 logically entail S3? Justify your answer: if you answered yes, show why the entailment holds, if you answered no, give a counterexample interpretation. (10 marks) Answer No, S1 and S2 do not logically entail S3. An interpretation which satisfies S1 and S2 but not S3 would be for example where all things break when they Collections: Computer Technologies and Information Sciences