Declarative representation of curricula models: an LTL- and UML-based approach Matteo Baldoni, Cristina Baroglio, Giuseppe Berio, and Elisa Marengo Dipartimento di Informatica — Universit` a degli Studi di Torino C.so Svizzera, 185 — I-10149 Torino (Italy) {baldoni,baroglio,berio}@di.unito.it elisa.mrng@gmail.com Abstract—In this work, we present a constrained-based rep- resentation for specifying the goals of “course design”, that we call curricula model, and introduce a graphical language, grounded into Linear Time Logic, to design curricula models which include knowledge of proficiency levels. Based on this representation, we show how model checking techniques can be used to verify that the user’s learning goal is supplied by a curriculum, that a curriculum is compliant to a curricula model, and that competence gaps are avoided. This proposal represents the most recent advancement of a work, carried on in the last years, in which we are investigating the use of both agents and web services for building and validating curricula. We also outline future research directions. I. I NTRODUCTION AND MOTIVATIONS As recently underlined by other authors, there is a strong relationship between the development of peer-to-peer, (web) service technologies and e-learning technologies [22]. The more learning resources are freely available through the Web, the more modern e-learning management systems (LMSs) should be able to take advantage from this richness: LMSs should offer the means for easily retrieving and assembling e- learning resources so to satisfy specific users’ learning goals, similarly to how (web) services are retrieved and composed [17]. In [6], we have shown the possibility of automatically composing SCORM [1] courseware by exploiting semantic web technology and, in particular, LOM annotations. More rcently [3], we have developed a reasoning service that has been integrated in the Personal Reader framework, a service- oriented learning platform. The reasoning service is basically a planner, which can build curricula in a goal-driven way, where the goal is a set of desired competences. The reasoner is invoked in a service-oriented fashion to help a user and build a curriculum. To this aim, the reasoner is fed with a set of initial competences that the user has, the competences that the user would like to acquire, and the URL of a repository of descriptions of courses, given as RDF triples. Besides building curricula, there are other interesting tasks that can be performed. Some of these concern curricula which are supplied directly by users. As in a composition of web services it is necessary to verify that, at every point, all the information necessary to the subsequent invocation will be available, in a learning domain, it is important to verify that all the competencies, i.e. the knowledge, necessary to fully understand a learning resource are introduced or available before that learning resource is accessed. The composition of learning resources, a curriculum, does not have to show any competence gap. Unfortunately, this verification, as stated in [15], is usually performed manually by the learning designer, with hardly any guidelines or support. A recent proposal for automatizing the competence gap verification is done in [22] where an analysis of pre- and post-requisite annotations of the Learning Objects (LO), rep- resenting the learning resources, is proposed. A logic based validation engine can use these annotations in order to validate the curriculum/LO composition. Melia and Pahl’s proposal is inspired by the CocoA system [12], that allows to perform the analysis and the consistency check of static web-based courses. Competence gaps are checked by a prerequisite checker for linear courses, simulating the process of teaching with an overlay student model. Pre- and post-requisites are represented as “concepts”. Together with the verification of consistence gaps, there are other kinds of verification. Brusilovsky and Vassileva [12] sketch some of them. In our opinion, two are particularly im- portant: (a) verifying that the curriculum allows to achieve the users’ learning goals, i.e. that the user will acquire the desired knowledge, and (b) verifying that the curriculum is compliant against the course design goals. Manually or automatically supplied curricula, developed to reach a learning goal, should match the “design document”, a curricula model, specified by the institution that offers the possibility of personalizing curricula. Curricula models specify general rules for designing sequences of learning resources (courses). We interpret them as constraints, that are expressed in terms of concepts and, in general, are not directly associated to learning resources, as instead is done for pre-requisites. They constrain the process of acquisition of concepts, independently from the resources. The availability of languages for designing curricula models, in a way that can automatically be processed by a reasoning system (be it an agent or a service) is a fundamental milestone in the development of checkers that perform the verifications described above, so to supply the the user and, when present, also the organization which supplies the courses, with a