Well-Gradedness of Knowledge Structures

Tests for the well-gradedness of knowledge structures.

kstructure_is_wellgraded(x)

Arguments

x	An R object of class kstructure.

Details

A knowledge structure is considered well-graded if any two of its states are connected by a bounded path, i.e., each knowledge state (except the state for the full set of domain problems Q) has at least one immediate successor state that comprises the same domain items plus exactly one and each knowledge state (except the empty set {}) has at least one predecessor state that contains the same domain items with the exception of exactly one.

kstructure_is_wellgraded takes an arbitrary knowledge structure and tests for its well-gradedness.

Value

A logical value.

References

Doignon, J.-P., Falmagne, J.-C. (1999) Knowledge Spaces. Heidelberg: Springer Verlag.

See also

kstructure

Examples

kst <- kstructure(set(set(), set("a"), set("b"), set("c"), set("a","b"), 
   set("b","c"), set("a","b","c")))
kstructure_is_wellgraded(kst)
#> [1] TRUE

kst <- kstructure(set(set(), set("a"), set("b"), set("c"), set("a","b"), 
   set("a","b","c")))
kstructure_is_wellgraded(kst)
#> [1] FALSE