# Gradation Property of Learning Paths

### Description

Tests for the gradation property of learning paths.

### Usage

1 |

### Arguments

`x` |
A |

### 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

1 2 3 4 5 6 | ```
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)
``` |