state2imp {DAKS}

Transformation from Knowledge States to Implications

Description

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

Usage

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.

Value

If the argument P is of required type, state2imp returns an object of class set (the surmise relation) representing the set of implications.

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.'

Author(s)

Anatol Sargin, Ali Uenlue

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 R package for data analysis methods in knowledge space theory. Journal of Statistical Software, 37(2), 1–31. URL http://www.jstatsoft.org/v37/i02/.

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)