zang: (( ))=

fu: ( )( )=( )

<#yypuz 5><t,w,f,x 3><n:{f,x} {t,f} {t} {f} {x} { }><y:*>auth 12ed1</yy>

Put the outcome catalog into columns. The pool of names—t,w,f,x—has 2^{4} = 16 combinations, and only those yielding on evaluating the hidden yy-gram are given explicity. The rest yield Yang, as the catalog says—<y:*>—so we reconstruct them for listing in our Yang column.

_{—some unseen yy-gram—}

{w}

{t,w,f,x}

{t,w,f}

{t,w,x}

{t,f,x}

{w,f,x}

{w,f}

{t,x}

{w,x}

{t,w}

Group the outcomes into pairs where you detect a deep or possibly bogus name. For example, the pair
**
{w,f,x}
{w,f}
**
shows that

A similar pair is
**
{t,w,f,x}
{t,w,f}
**

Among the **x**, namely
**
**

{f}, {f,x} _{and} {x}, { }

Let's make a fresh catalog listing with pairs differing only in **x**:

_{—some unseen yy-gram—}

{w,x}, {w}

{t,w,f,x}, {t,w,f}

{w,f,x}, {w,f}

---

{t,w,x}

{t,f,x}

{t,x}

{t,w}

Below the tick --- we fail to convict **x** bogus. In particular, the pair **{t}, {t,x}** shows **x** affecting the outcome.

Our solution yy-gram must therefore include **x**.

This interpretation on the catalog information suggests treating another name to discriminatory pairing. To choose a candidate, give attention below the tick.

There we see outcomes where **f** often fails to make a difference:

_{—some unseen yy-gram—}

{t,w,f,x}, {t,w,x}

{t,f,x}, {t,x}

{w,f,x}, {w,x}

{t,w,f}, {t,w}

{w,f}, {w}

---

The new cataloguing shows no case where **f** affects the outcome. This is what we understand by a *bogus* name. A yy-gram solution to this outcome catalog does not have to involve **f**.

Accordingly we make a fresh catalog listing of only those valuation there-lists that do not mention **f**:

_{—some unseen yy-gram—}

{t,w,x}

{t,x}

{w,x}

{t,w}

{w}

The task ahead is to infer a yy-gram with the catalogued and now clarified i/o behavior.

We note that **x** alone nor **t** alone is insufficient for a yang outcome. This puts those two names deeper than the outer milieu in any solution yy-gram.

Another analysis on these two names is to ask, is presence of either sufficient to force a

outcome?Evidently not, from an inspection of the yang column. This in turn allows the conclusion that both are deeper in any solution yy-gram than depth 1, counting the outermost space as depth 0.

This brings to mind the AND form, conjunction, in logic interpretation:
**
a AND b <—>
( ^{(a)(b)}), where the names in conjunction are at depth 2.
**

Now we address the yang column. Let's group the outcomes, segregating the valuations according to the remaining name in the clarified pool, **w**:

_{—some unseen yy-gram—}

{t,w,x}

{w,x}

{t,w}

{w}

---

{t,x}

Manifestly, yang-presence of **w** is sufficient to force a ( ) outcome .

Independently of that, [**t** AND **x**] is likewise sufficient to force a ( ) outcome.

We are familiar enough with interpreting yy-grams for logic that we can now read the yang column as

"[ **t** AND **x** ] OR **w**""

—grouping moieties with square brackets [ ] so as not to presume the artificial boolean rules for binding.

Expressing these conclusions together in a yy-gram:

(^{(t)(x)})w

This solution might appear in tweet format as

<#yygram 5> <ans: ((t)(x))w > auth 12ed1</yy>

or as

<#yygram 5> <ans: w((x)(t)) > auth 12ed1</yy>

or some other equivalent differing only in order within or outside enclosers.

©2012 David Zethmayr

update 2012.4.10