state2imp {DAKS} | R Documentation |
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)
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. |
If the argument P
is of required type, state2imp
returns an object of class set
(the surmise
relation) representing the set of implications.
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.'
Anatol Sargin anatol.sargin@math.uni-augsburg.de, Ali Uenlue ali.uenlue@math.uni-augsburg.de
Doignon, J.-P. and Falmagne, J.-C. (1999) Knowledge Spaces. Berlin, Heidelberg, and New York: Springer-Verlag.
Sargin, A. and Uenlue, A. (2009) DAKS: An R package for data analysis in knowledge space theory. Manuscript submitted for publication. http://www.math.uni-augsburg.de/~uenlueal/
imp2state
for transformation from implications to
knowledge states. See also DAKS-package
for general
information about this package.
## 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)