Computer Science and Information Technology 1(2): 125-131, 2013 http://www.hrpub.org DOI: 10.13189/csit.2013.010208 Generation of Questions Sequences in Intelligent Teaching Systems Based on Algebraic Аpproach Alexander Zuenko 1 , Alexander Fridman 1,* , Boris Kulik 2 1 Institute for Informatics and Mathematical Modeling, Kola Science Centre of the Russian Academy of Sciences (RAS), 24A Fersman str., 184209, Apatity, Russia 2 Institute of Problems in Machine Science of the RAS, 61 Bol’shoi pr., 199178 St. Petersburg Russia *Corresponding Author: fridman@iimm.kolasc.net.ru Copyright © 2013 Horizon Research Publishing All rights reserved. Abstract The paper describes an approach to development of question-and-answer teaching systems based on controlled languages and algebraic models for representation and processing of question-and-answer texts. We propose using a partial order relation "question-subquestion" to build an individual trajectory of teaching. To model a strategy of examination, we use defeasible reasoning formalized within our earlier developed QC-structures. Keywords Intelligent Teaching System, Question-and-answer Text, QC-structure, N-tuple Algebra 1. Introduction There are four main parts in intelligent teaching systems (ITS), namely teaching material, a teaching unit, a knowledge control unit and a check unit [1]. Here we consider the last two units only. The knowledge control unit analyses how a student has learned the material, the check unit evaluates knowledge of a student and puts a mark. Separating the knowledge control unit from the check unit allows determining the part of knowledge that the student lacks. In some ITSs, the knowledge control unit is included either in the teaching unit or in the check unit. Papers dealing with ITSs mostly introduce ideas how check systems can determine abilities of a student by analyzing his decisions [2]. Such systems focus on putting a mark. Unlike these systems, when a teacher gets a wrong answer, he/she tries to reveal vacancies in the student's knowledge by putting leading questions or additional tasks. As a result, the teacher either "leads" the student to the right answer or determines the concept, rule or theorem, which the student does not know or cannot use. In the authors' opinion, an ITS should work more as a real teacher. Correspondingly, the ITS is not to only estimate the degree of knowledge for a student, but also to reveal poorly perceived knowledge and to advise ways for its improving. An ITS controls a question-and-answer dialog to appraise student's knowledge. The unit simulating teacher's examination strategies plays an important role in this dialog. It also provides revision of estimates of student's knowledge accumulated during examination. The situation becomes more complicated when this dialog stipulates natural language communication with "arbitrary" shapes of answers. The term "arbitrary" is not quite correct as the student is supposed to be familiar with the teaching material i.e. immersed into the context. This means the student ought to give reasonable answers within the terminology relevant to the teaching material. Lately, CNLs (Controlled Natural Languages) are mostly popular for development of dialog systems admitting arbitrary answers of users. A CNL is a version of a natural language simplified by means of a problem-methodological context and created for solving of certain tasks [3]. An original variant of a CNL for question-and-answer dialogs controlled by conceptual grammars was proposed in [4]. A semantical classification of question-and-answer texts was given there as well. In this paper, we propose an approach to building ITSs based on an algebraic interpretation of the mentioned model of the question-and-answer dialog. We use our n-tuple algebra (NTA) [5-7] and an extension of partially ordered sets, namely QC-structures [8], to represent and analyze question-and-answer texts. Let us now briefly describe NTA [5-7]. 2. Basics of N-tuple Algebra N-tuple algebra was developed for modeling and analyzing of n-ary relations. Unlike relational algebra that is used for formalization of databases, NTA can use all laws and techniques of mathematical logic for logical modeling and analysis of systems, namely logical inference, corollary verification, analysis of hypotheses, abductive inference, etc. NTA is an algebra of n-ary relations based on features of