By Johnson H.W.
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Extra info for High-speed digital design.A handbook of black magic
A parse tree representing a well-formed formula. and this matter by being very observant. ); but the only time we can put a ')' to the right of something is if that something is a well-formed formula (again, check all the v pq + is not well-formed. rules to see that this is so). Thus, (l)() 1) Probably the easiest way to verify whether some formula 4 is well-formed is by trying to draw its parse tree. In this way, you can verify that the formula (((lp)A q) + (p A (q V (lr)))) above is well-formed.
We were deliberately informal about that, for our main focus was on trying to understand the precise mechanics of the natural deduction rules. However, it should have been clear that the rules we stated are valid for any formulas we can form, as long as they match the pattern required by the respective rule. 3 Propositional logic as a formal language standing for generic formulas. Yet, it is time that we make precise the notion of 'any formula we may form'. 2) an easy formalism for specifying well-formed formulas.
Naturally, it is sensible to open a box only when you know which rule you are going to use to close it. O K , but how do we actually go about constructing a proof? You write the premises at the top of your page and the conclusion at the bottom. Now, you're trying to fill in the gap, which involves working simultaneously on the premises (to bring them towards the conclusion) and on the conclusion (to massage it towards the premises). Look first at the conclusion. This means drawing a box with 4 at the top and y at the bottom.