Well-founded semantics
Template:Short description Script error: No such module "about". 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.[1][2] The Prolog system XSB implements the well-founded semantics since 1997.[3][4]
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.[1]
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).
b :- not(a).
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.[5]
Complexity
In 1989, Van Gelder suggested an algorithm to compute the well-founded semantics of a propositional logic program whose time complexity is quadratic in the size of the program.[6] Template:As of, no general subquadratic algorithm for the problem was known.[7]
References
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- ↑ Przymusinski, Teodor. Well-founded Semantics Coincides with Three-Valued Stable Semantics. Fundamenta Informaticae XIII pp. 445-463, 1990.
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