Problem Detail: I have a formula $ neg((q implies neg q) vee p vee (neg q implies (r wedge p))) $. As it contains 3 subformulas between the $vee$’s, how can i put it into a parse tree, as a parse tree contains 2 branches from each node.
Asked By : AkshaiShah
Answered By : Raphael
As it is, your formula is ambiguous; it is not clear which pair of parentheses to insert in order to get a binary tree. Both $qquad displaystyle varphi_1 lor (varphi_2 lor varphi_3)$ and $qquad displaystyle (varphi_1 lor varphi_2) lor varphi_3$ are feasible. Luckily for you, $lor$ is associative, so you can choose either one: 
[source] For the purposes of parsing, you would either require formulae to be completely parenthesised, or specify operators to be left- (or right-) associative. Operator precedences would be the next thing to look into, in order to disambiguate formulae like $qquad displaystyle a land b lor c$.
[source] For the purposes of parsing, you would either require formulae to be completely parenthesised, or specify operators to be left- (or right-) associative. Operator precedences would be the next thing to look into, in order to disambiguate formulae like $qquad displaystyle a land b lor c$.
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Question Source : http://cs.stackexchange.com/questions/4918
