Well-founded semantics
In computer science, the well-founded semantics is a three-valued semantics for logic programming, which gives a precise meaning to general logic programs.
History
The well-founded semantics was defined by Van Gelder, et al. in 1988. The Prolog system XSB implements the well-founded semantics since 1997.Three-valued logic
The well-founded semantics assigns a unique model to every general logic program. However, instead of only assigning propositions true or false, it adds a third value unknown for representing ignorance.A simple example is the logic program that encodes two propositions
a and b, and in which a must be true whenever b is not and vice versa:a :- not.
b :- not.
neither
a nor b are true or false, but both have the truth value unknown. In the two-valued stable model semantics, there are two stable models, one in which
a is true and b is false, and one in which b is true and a is false.Stratified logic programs have a 2-valued well-founded model, in which every proposition is either true or false. This coincides with the unique stable model of the program. The well-founded semantics can be viewed as a three-valued version of the stable model semantics.