getKFringe: Outer and Inner Fringes of a Knowledge Structure

Description

Returns the outer or inner fringe for each state in a knowledge structure.

Usage

getKFringe(K, nstates = nrow(K), nitems = ncol(K), outer = TRUE)

Value

A state-by-problem indicator matrix representing the outer or inner fringe for each knowledge state in K.

Arguments

K: a state-by-problem indicator matrix representing the knowledge structure. An element is one if the problem is contained in the state, and else zero.
nstates: the number of knowledge states in K.
nitems: the number of items in K.
outer: logical. If TRUE return outer fringe, else return inner fringe.

Details

The outer fringe of a knowledge state is the set of all items that can be learned from that state, such that adding an outer-fringe item to the state results in another state in K,

$$K^O = \{q \notin K | K \cup \{q\} \in \mathcal{K}\}.$$

The inner fringe of a knowledge state is the set of all items that have been learned most recently to reach that state, such that deleting an inner-fringe item from the state results in another state in K,

$$K^I = \{q \in K | K - \{q\} \in \mathcal{K}\}.$$

Examples

Run this code

data(DoignonFalmagne7)

## Which items can be learned from each state?
getKFringe(DoignonFalmagne7$K)

## Which items in each state have been recently learned?
getKFringe(DoignonFalmagne7$K, outer = FALSE)