Gradation Property of Learning Paths

Tests for the gradation property of learning paths.

lpath_is_gradation(x)

Arguments

x	A list of learning paths .

Details

A learning path is considered a gradation if each state in a learning path differs from its predecessor and/or successor state by a single item/notion.

lpath_is_gradation takes an arbitrary list of learning paths and tests for their gradation property.

Value

A list of logical values where each element represents one learning path.

References

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

See also

kstructure, lpath

Examples

kst <- kstructure(set(set(), set("c"), set("a","b"), set("b","c"), 
   set("c","d"), set("d","e"), set("a","b","c"), set("b","c","d"), 
   set("c","d","e"), set("a","b","c","d"), set("a","b","d","e"), 
   set("b","c","d","e"), set("a","b","c","d","e")))
lp <- lpath(kst)
lpath_is_gradation(lp)
#> [[1]]
#> [1] FALSE
#> 
#> [[2]]
#> [1] TRUE
#> 
#> [[3]]
#> [1] TRUE
#> 
#> [[4]]
#> [1] TRUE
#> 
#> [[5]]
#> [1] FALSE
#> 
#> [[6]]
#> [1] FALSE
#> 
#> [[7]]
#> [1] TRUE
#> 
#> [[8]]
#> [1] TRUE
#> 
#> [[9]]
#> [1] TRUE
#> 
#> [[10]]
#> [1] FALSE
#>