Learning-Oriented Question Recommendation Using Bloom’s Learning Taxonomy and Variable Length Hidden Markov Models - Transactions on Large-Scale Data-and Knowledge-Centered Systems - page 32

2.1 Knowledge Base

Let be a set of questions from a particular domain. In general, QA systems

can cover several domains of interest, but, for simplicity, we will consider in the
following only a single domain.

Q

The Domain-Specific Taxonomy. Let T be a set of predefined topics from

a particular domain. In general, . The structure of the corresponding

topic taxonomy is given by a generalization-specification relationship between
topics:

|Q| |T |

PↆT ×T , ( ˄ i ,˄ j ) ∈P ⃒⃐ ˄ i parent of ˄ j , (1)

where ˄ i ,˄ j ∈T .

Fig. 1. Snapshot of an example nutrition taxonomy

Consider also a mapping relationship between Q and T , which maps to each

question q . A mapping ( q, ˄ ) has the following meaning:

“question q is about topic ˄ “. We will further refer to this relationship as topic
mapping and it is defined in the following way:

∈Q a topic ˄ ∈T

M ˄ ↆQ×T , ( q, ˄ ) ∈M ˄ ⃒⃐ q is mapped to topic ˄. (2)

M ˄ is a surjection with respect to Q (i.e. all questions
are mapped to at least one topic). Moreover, one question can be mapped to
several topics and one topic can map several questions (see Figure 2 ).

The topic mapping

The Learning Taxonomy. Additionally, we enrich the knowledge base with
learning objectives, as defined in Bloom's taxonomy [ 2 ]. Let L be the set of

all learning objectives. Every learning objective ˆ ∈L is defined as a pair of

knowledge and cognitive process instances ( ʺ, ˁ ) ∈K×C , where

K { factual, conceptual, procedural, metacognitive }

= (3)