[Fuzzy-tg] Fuzzy RuleML telecon -- RIF Core Design: Ordering truth values

[Boley, Harold]

RIF Core Design
http://www.w3.org/2005/rules/wg/wiki/Core


Positive Conditions
http://www.w3.org/2005/rules/wg/wiki/Core/Positive_Conditions

Semantic Structures
The set TV has a total or partial order, called the truth order; it is
denoted with <t. In RIF Core, f <t t, and it is a total order. (See end
note on ordering truth values
<http://www.w3.org/2005/rules/wg/wiki/Core/EndNotes#Note2.1-3> .)


Notes on Semantic Structures
http://www.w3.org/2005/rules/wg/wiki/Core/EndNotes



Truth values: Some RIF dialects will have additional truth values. For
instance, some versions of NAF use three truth values: t, f, and u
(undefined). Handling of contradictions and uncertainty requires at
least four truth values: t, u, f, and i (inconsistent). 

Ordering truth values: In the well-founded semantics for NAF, f <t u <t
t, and it is again a total order. But in four-valued logics, which are
often used for dealing with uncertain or inconsistent information, the
truth order is partial: f <t u <t t and f <t i <t t. Such logics also
have another partial order, called the knowledge order <k: u <k t <k i;
and u <k f <k i. Under the knowledge order, true and false are
incomparable, and facts that are both true and false receive the truth
value i, which is the least upper bound of f and t in the knowledge
order.

 

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