state2imp function

Transformation from Knowledge States to Implications

state2imp transforms a set of knowledge states (ought to be a quasi ordinal knowledge space) to the corresponding set of implications (the surmise relation).

state2imp(P)

Arguments

• P: a required matrix of ones and zeros giving the knowledge states to be used. Each row represents the $1$/$0$-pattern of a knowledge state.

Returns

If the argument P is of required type, state2imp

returns an object of class set (the surmise relation) representing the set of implications.

References

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

Uenlue, A. and Sargin, A. (2010) DAKS: An package for data analysis methods in knowledge space theory. Journal of Statistical Software, 37 (2), 1--31. URL http://www.jstatsoft.org/v37/i02/.

Author(s)

Anatol Sargin, Ali Uenlue

Note

For any set of knowledge states the returned binary relation is a surmise relation. In case of a quasi ordinal knowledge space this is Birkhoff's theorem. For details refer to Doignon and Falmagne (1999, Theorem 1.49) .

A set of implications, an object of the class set, consists of $2$-tuples $(i, j)$ of the class tuple, where a $2$-tuple $(i, j)$ is interpreted as `mastering item $j$ implies mastering item $i$.'

See Also

imp2state for transformation from implications to knowledge states. See also DAKS-package for general information about this package.

Examples

## an arbitrary matrix of knowledge states is defined
x <- matrix(0, nrow = 5, ncol = 3)
x[1, ] <- c(0, 0, 0)
x[2, ] <- c(0, 0, 1)
x[3, ] <- c(0, 1, 0)
x[4, ] <- c(0, 1, 1)
x[5, ] <- c(1, 1, 1)

state2imp(x)