Re: All hail Neo!
Date: Mon, 01 May 2006 23:38:44 GMT
Message-ID: <8_w5g.24847$mh.10958_at_tornado.ohiordc.rr.com>
Marshall Spight wrote:
> Jay Dee wrote: >
>>Marshall Spight wrote:
>>
>>>Jay Dee wrote:
>>>
>>>
>>>>Marshall Spight wrote:
>>>>
>>>>
>>>>>Bob Badour wrote:
>>>>>
>>>>>
>>>>>
>>>>>>If one starts with a two valued logic and adds a third value, one
>>>>>>changes all of the features of the prior logic. Every truth table must
>>>>>>change. Every identity is potentially affected as are associativity,
>>>>>>distributivity etc.
>>>>>
>>>>>Do the pre-existing rows of the truth tables of existing
>>>>>boolean functions change?
>>>>
>>>>Yes; columns and rows are added. The result is the "combinatorial
>>>>explosion" referred to elsewhere.
>>>
>>>
>>>Columns are added to the truth tables of existing boolean functions,
>>>you say? Can you give an example? The columns of the truth table
>>>for a boolean function correspond to the input and output parameters
>>>of that function, so saying column are added is saying that there
>>>are additional arguments or result values. This is certainly not
>>>true for AND and OR; can you give an example of a boolean function
>>>for which it is true?
>>>
>>>And the assertion that "rows are added" does not make
>>>a "yes" answer to my question. Adding rows does not
>>>change the pre-existing rows.
>>>
>>>I know what the combinatorial explosion is, and it's one reason
>>>why I argue against the use of 3VL in language design.
>>>
>>>
>>>Marshall
>>>
>>
>>
>>(using a monospace font...)
>>
>>and| T | F
>>---+-------
>> T | T | F
>> F | F | F
>>
>>must become
>>
>> and| T | F | null
>>----+-------------
>> T | T | F | ?
>> F | F | F | ?
>>null| ? | ? | ?
>>
>>more columns, more rows.
> > > Ah, I see. You are using a structure for the truth table > where each axis is a parameter. That is perfectly valid, > but it is not how I structure them, so we are talking > past each other.
Okay, then, with the nullary operators,
n0 n1
T F
the unary operators
u0 u1 u2 u3
---+---------------
T | T T F F
F | T F T F
(where u1 is identity, u2 is negation, and u0 and u3 are anonymous), the "big six" binary operators
/\ \/ -> <- = <>
---+----------------------- TT | T T T T F... TF | F T F T F...
FT | F T T ...
FF | ...
and the sole ternary operator ("if, then, else") we find useful:
(conditional composition?)
---+------------------- TTT| T
TTF| T
TFT| F
...
(I've also seem these sets named niladic, monadic, dyadic, &c.)
> I prefer all the parameters (in and out both) as columns; > it generalizes better to n-ary functions.
(Sorry, I've got the "in and out both" as rows.)
I don't see how adding a third value could result in anything other than an explosion of rows, columns, or rows and columns.
> Anyway, it appears we all agree "NVL bad".
Both "n-VL | n <> 2" and the SQL-ish "NVL(..., ...)" are... Bad? Hmm, that doesn't seem to be sufficiently judgmental.
> > Marshall >Received on Tue May 02 2006 - 01:38:44 CEST