# Well-Gradedness of Knowledge Structures

### Description

Tests for the well-gradedness of knowledge structures.

### Usage

1 |

### Arguments

`x` |
An |

### 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

1 2 3 4 5 6 7 | ```
kst <- kstructure(set(set(), set("a"), set("b"), set("c"), set("a","b"),
set("b","c"), set("a","b","c")))
kstructure_is_wellgraded(kst)
kst <- kstructure(set(set(), set("a"), set("b"), set("c"), set("a","b"),
set("a","b","c")))
kstructure_is_wellgraded(kst)
``` |