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 3.1

 

1.

Which of the following sequents is correct? Where the sequent is incorrect, give a counterexample.
 
(i)
[PQ] |= [PQ]
 
(ii)
[PQ] |= [PQ]
 
(iii)
[PQ] |= [PQ]
 
(iv)
[PQ], [RQ] |= [[PR]Q]
 
(v)
[[PQ] [RQ]] |= [[PR]Q]
 
(vi)
|= [[PQ][PQ]]
 
(vii)
|= [[PQ][QP]]
 
(viii)
[PP] |= Q
 
(ix)
Q |= [PP]
 
Answers

 

 

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