Chapter Five, Tutorial Eight

SD+: Strategy

The main point about strategy in SD+ is a quite simple:

Apply one of the new rules if its use is obvious, but *only*
if it will help move the derivation toward one of your goals.

We make the point this way because the new rules are so powerful that they can be dangerous! Well, they do allow you to very efficiently derive conclusions; but if you apply them randomly, they may take you far from your goals. So, in this tutorial we need to emphasize how they can be best applied.

Let's begin with just a few examples.

Now, we should look at some derivations putting these rules together. Here's
a **demonstration**
to get us started. ** Our goal will be to derive '~LvM'**.

First, look to the *goal, '~LvM'*

Your first thought may be to use vI. But this will *not* work! It's
not obvious at first, but there is no way to derive either disjunct.

In SD you would have to give up on vI after awhile and use ~E.

But in SD+ there are alternatives. You might notice that a component of line 2 is equivalent to the goal!

So, one might prepare for *later* use of =E
by *now* applying DM to line 1.

Notice that line 1 is of the form '~(QvR)'. It's one of our ways of saying "neither...nor". So, no surprise that we can get line 3 which is of the form '~P&~Q'.

Now we may simply apply &E to line 3. But which conjunct will be useful
in getting to our goal?

We must be careful not to get carried away. We could derive '~(D=~T)', then do EQ, then DM and DN and on and on. Think about it. But these moves will not lead toward our goal!

We derived line 4 so that we could now apply =E.

Remember, we saw that the second bicomponent of 2 was equivalent to our goal.

Finally, we can apply IM and finish.

It will take awhile to get used to these new rules. But once you do, steps like these will seem obvious.