Basic Functions in Knowledge Space Theory Using Matrix Representation
Perform a probabilistic knowledge assessment
Update probability distribution applying Bayesian update
Determine next question for probabilistic knowledge assessment
Determine next question for probabilistic knowledge assessment
Simulate assessments for a set of response patterns
Update probability distribution applying multiplicative rule
Determine the basis for a surmise function
Determine the basis of a knowledge space from a surmise relation
Compute the basis of a knowledge space
Generic kmbasis() function
Determine a color vector based on probabilities
Compute the distance between a data set and a knowledge structure
Test two double numbers on equity with a certain tolerance
Reduce a family of knowledge states with respect to item equivalence
Convert a binary matrix to a kmfamset object (family of sets)
Compute the fringe of a state within a knowledge structure
Generate a knowledge structure from a set of response patterns
Determine all gradations between two states
Convert an IITA result into a surmise relation matrix
Check for wellgradedness of a knowledge structure
Determine all learning paths in a knowledge structure
Compute the neighbourhod of a state within a knowledge structure
Compute the n-neighbourhod of a state within a knowledge structure
Determine the notions of a knowledge structure
Test if a state is contained in a family of states
Derive a basis from a surmise function
Simulate a set of response patterns according to the BLIM
Convert a binary matrix to a kmspace object
Determine the basis of a knowledge space from a surmise relation
Validate a surmise relation against a data set
Convert a binary matrix to a kmstructure object
Compute the surmise function for a knowledge space or basis
Compute the surmise relation of a quasi-ordinal knowledge space
Compute the symmetric set difference between two sets
Create trivial knowledge spaces
Close a family of sets under union
Validate a knowledge structure against a data set
Plot a Hasse diagram
Knowledge space theory by Doignon and Falmagne (1999) <doi:10.1007/978-3-642-58625-5> is a set- and order-theoretical framework, which proposes mathematical formalisms to operationalize knowledge structures in a particular domain. The 'kstMatrix' package provides basic functionalities to generate, handle, and manipulate knowledge structures and knowledge spaces. Opposed to the 'kst' package, 'kstMatrix' uses matrix representations for knowledge structures. Furthermore, 'kstMatrix' contains several knowledge spaces developed by the research group around Cornelia Dowling through querying experts.