logic programming Logic programming is a programming paradigm which is largely based on formal logic. Any program written in a logic programming language is a set of sentences in logical form, expressing facts and rules about some problem domain. Major logic pro ...

, the well-founded semantics is one definition of how we can make conclusions from a set of logical rules. In logic programming, we give a computer a set of facts, and a set of "inference rules" about how these facts relate. There are several different ways that we might want the computer to apply these rules; the well-founded semantics is one of these ways.

History

The well-founded semantics was defined by Van Gelder, et al. in a 1991 paper.

Relations to other models

The well-founded semantics can be viewed as a three-valued version of the stable model semantics.Przymusinski, Teodor.
Well-founded Semantics Coincides with Three-Valued Stable Semantics
'. Fundamenta Informaticae XIII pp. 445-463, 1990. Instead of only assigning

proposition In logic and linguistics, a proposition is the meaning of a declarative sentence. In philosophy, " meaning" is understood to be a non-linguistic entity which is shared by all sentences with the same meaning. Equivalently, a proposition is the no ...

s ''true'' or ''false'', it also allows for a value representing ignorance. For example, if we know that


Specimen A is a moth if specimen A does not fly during daylight.

but we do not know whether or not specimen ''A'' flies during the day, the well-founded semantics would assign the proposition ``specimen A is a moth`` the value ''bottom'' which is neither ''true'' nor ''false''.

Applications

The well-founded semantics is also a way of making safe inferences in the presence of contradictory data such as noisy data, or data acquired from different experts who may posit differing opinions. Many two-valued semantics simply won't consider such a problem state workable. The well-founded semantics, however, has a built-in mechanism to circumvent the presence of the contradictions and proceeds to derive as many two-valued facts as possible, even though some consequences may remain unknown.

Complexity and algorithms

The fastest known algorithm to compute the WF-Semantics in general, is of quadratic complexity.

References

Logic programming {{formalmethods-stub