Tutorial Contents Tutorial Three: Propositional Calculus: Tableaux - The Sentence Tableaux Rules - Testing Arguments for Validity - Sequents - Syntactic Sequents - Semantic Sequents - Soundness and Completeness - Correctness of Sequents and Validity of Arguments
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Exercise 4.2

 

1.

Provide formalisations of the sentences below using the following domain and interpretation:

  Domain: everything
  a: John
  Exy: x is an exam taken by y
  Ux: x is an undergraduate
  Dx: x got a degree
  Pxy: x passed y
  Hxy: x worked harder than y

 

  (i) No undergraduate who worked less hard than John got a degree
  (ii) If undergraduates passed all their exams they got a degree
  (iii) [John worked harder than any undergraduates who did not pass all their exams
  (iv) Only undergraduates who worked harder than John got a degree and even some of those didn't, though some did.
 
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