In general programming languages, like java, C# etc. use dichotomic logic.
Perhaps it is not necessary, however three-valued logic can be more expressive and will improve readability. See an example:
Consider a function F(s) returning "true" if "s" is a unicode string or false if it is an ISO-8859 one. If s = "René", then F(s) is true provided that 'é' is codified by means of two bytes, or it is false whenever only one byte denotes 'é'.
By contrast, if all characters in the string s have a code less than 128, then we cannot discern whether it is codified ISO or unicode. In this case, a third truth-value, between true and false, assigned to to F(s) would be more expressive.
The R (statistical) programming language allows logical variables to take the values true, false, and NA (not available). It has a sensible extended definition of the logical operations and, or, not: sensible according to intended interpretation of the third truth value. Unfortunately there are other three-valued logics which make sense with different interpretations of the third value. For instance, Thomas Cool proposes a three-valued logic where the third value stands for "neither true nor false, because the question is meaningless". That is rather different from what you would want when the third value simply means "true or false - status unknown".
Ternary computing was pushed in Russia in the late 1950s, and even here in the US as late at 1973, but binary computing was mass produced and more efficient (http://en.wikipedia.org/wiki/Ternary_computer).
The question then becomes implementing a ternary approach on top of a binary machine. One would think that while possible, the extra work required to differentiate between a positive vs a mostly positive result - or a negative vs a mostly negative result would slow things down. Which begs the question of whether or not something that is mostly positive (but not 100%) the same result as something that is mostly negative (but also not 100%)?
I mostly agree. Binary machines can simulate very complex systems, even neural networks where each simulated "neuron" can give an output weighted over a continuous sine range. You just need to code the functions that give a proper value of your desired range of outputs in response to a known range of inputs.
But it is an interesting question since it seems that coming technologies as quantum computers will expand a lot hardware processing constraints so new low level programming languages will be needed to handle "hardware logic", e.g. qbit.
In the programming language Ruby logical expressions have values 'true', 'false', or 'nil'. Just as Juan mentioned in his explanation of the question, there are situations in which a result 'nil' gives more valuable information than a result 'false'. This is simply a matter of (intelligent) language definition and has nothing to do with 'ternary computing' mentioned in earlier contributions. --- Now I become aware of the contribution of Richard Gill, where similar statements are being made concerning the language R.
Peter,
you lift the discussion to a level to which it does not belong. The convenience that Ruby offers to a programmer by letting some of its functions return 'nil' for some arguments should not be sacrificed in view of potentially ill-mannered mathematical logicians.
BTW, "don't know" is certainly not the intended meaning of 'nil' in Ruby. Better: A evaluates to nil whenever both 'A is true' and 'A is false' are misleading or unacceptable as statements.
Peter,
of course, Ruby has a definition for the standard logical connectives including logical value 'nil'. The plausibility arguments for this specific definition to be found in my (only) Ruby book (Dave Thomas: Programming Ruby) may not be the arguments of the creator of the language. So I will not try to do justice to this particular fixation and refer you to Ruby which is fully accessible in the web.
Your last question is simple: As it stands it is not Ruby since true,false,nil are constants. If you replace your DK by a logical expression, which by definition evaluates to either true, false, or nil then, in case of nil you take A and in case of true or false you take B.
In the cases of the example, standard Fuzzy Logic (many-valued logic - http://en.wikipedia.org/wiki/Fuzzy_logic ) could also be an option. It will still give a high match on the special characters. Using a probabibility on similarity you can easily estimate if it is likely the same (intended) word. This also works with typo's or other small problems in a string.
Peter,
in the cited book I find:
nil and true = true and nil = nil
false or nil = nil
nil or false = false
and the interesting sentence:
'Ruby has a simple definition of truth. Any value that is not nil or the constant false is true.'
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