Knowledge Space Theory

This document explains algorithms and basic operations of knowledge structures and knowledge spaces available in R through the kst package. Knowledge Space Theory (Doignon and Falmagne, 1999) is a set-theoretical framework, which proposes mathematical formalisms to operationalize knowledge structures in a particular domain. The most basic assumption of knowledge space theory is that every knowledge domain can be represented in terms of a set of domain problems or items. Moreover, knowledge space theory assumes dependencies between these items in that knowledge of a given item or a subset of items may be a prerequisite for knowledge of another, more difficult or complex item. These prerequisite relations are realized by surmise relations, which create a quasi-order between different items. One advantage of these surmise relations is that they reduce the quantity of all possible solution patterns to a more manageable amount of knowledge states. Each of these knowledge states represents the subset of items an individual is capable of solving. The collection of all knowledge states captures the organization of the domain and is referred to as knowledge structure. 1 Knowledge Structures The kstructure() function in package kst is the basic constructor for knowledge structures. It takes an endorelation representing a surmise relation or a set of sets each representing one knowledge state (e.g., one clause of a surmise system) and returns the corresponding knowledge structure: > kst kstructure(kst) {{"3"}, {"4"}, {"2", "3", "4"}, {"1", "2", "3", "4"}} > kst kst {{"a"}, {"a", "b"}, {"a", "c"}, {"d", "e"}, {"a", "b", "d", "e"}, {"a", "c", "d", "e"}, {"a", "b", "c", "d", "e"}} Note that by default the quotes indicate the fact that the items are represented by characters. For displaying purposes, these quotes may be turned off: > sets_options("quote", FALSE) > kst